Dual rack and pinion rotational inerter system and method for damping movement of a flight control surface of an aircraft

ABSTRACT

There is provided a dual rack and pinion rotational inerter system for damping movement of a flight control surface of an aircraft. The system has a flexible holding structure disposed between the flight control surface and a support structure of the aircraft. The system has a dual rack and pinion assembly held by and between the flexible holding structure. The dual rack and pinion assembly has a first rack, a second rack, and a pinion engaged to and between the racks. The system has a first terminal coupled to the first rack and coupled to the flight control surface, via a pivot element, and a second terminal coupled to the second rack, and coupled to the support structure. The system has a pair of inertia wheels adjacent the flexible holding structure. The system has an axle element inserted through the inertial wheels, the flexible holding structure, and the pinion.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation-in-part application of andclaims priority to pending U.S. patent application Ser. No. 15/159,706,filed May 19, 2016, entitled “Rotational Inerter and Method for Dampingan Actuator”, the content of which is incorporated herein by referencein its entirety, and the present continuation-in-part application isrelated to contemporaneously filed continuation-in-part, nonprovisionalU.S. patent application Ser. No. 15/867,940, titled “TranslationalInerter Assembly and Method for Damping Movement of a Flight ControlSurface”, filed on Jan. 11, 2018, the content of which is incorporatedby reference in its entireties.

FIELD

The present disclosure relates to actuators and, more particularly, to adual rack and pinion rotational inerter system and method for dampingmovement of a flight control surface of an aircraft.

BACKGROUND

Aircraft typically include a flight control system for directional andattitude control of the aircraft in response to commands from a flightcrew or an autopilot. A flight control system may include a plurality ofmovable flight control surfaces such as ailerons on the wings for rollcontrol, elevators on the horizontal tail of the empennage for pitchcontrol, a rudder on the vertical tail of the empennage for yaw control,and other movable control surfaces. Movement of a flight control surfaceis typically effected by one or more actuators mechanically coupledbetween a support structure (e.g., a wing spar) and the flight controlsurface (e.g., an aileron). In many aircraft, the actuators for flightcontrol surfaces are linear hydraulic actuators driven by one or morehydraulic systems which typically operate at a fixed working pressure.

One of the challenges facing aircraft designers is preventing theoccurrence of flutter of the flight control surfaces during flight.Control surface flutter may be described as unstableaerodynamically-induced oscillations of the flight control surface, andmay occur in flight control systems where the operating bandwidth of theflight control system overlaps the resonant frequency of the flightcontrol surface. Unless damped, the oscillations may rapidly increase inamplitude with the potential for undesirable results, includingexceeding the strength capability of the mounting system of the flightcontrol surface and the actuator. Contributing to the potential forcontrol surface flutter is elasticity in the flight control system. Forexample, hydraulic actuators may exhibit a linear spring response underload due to compressibility of the hydraulic fluid. The compressibilityof the hydraulic fluid may be characterized by the cross-sectional areaof the actuator piston, the volume of the hydraulic fluid, and theeffective bulk modulus of elasticity of the hydraulic fluid.

One method of addressing control surface flutter involves designing theflight control system such that the operating bandwidth does not overlapthe resonant frequency of the flight control surface, and may includelimiting the inertia of the load on the actuator and/or increasing thepiston cross-sectional area as a means to react the inertia load.Unfortunately, the above known methods result in an actuator system thatis sized not to provide the actuator with static load-carryingcapability, but rather to provide the actuator with the ability to reactlarger inertia as a means to avoid resonance in the operating bandwidth.As may be appreciated, limiting control surface inertia corresponds to adecrease in control surface area. A decrease in the surface area ofhigher inertia control surfaces of an aircraft empennage may reduce theattitude controllability of the aircraft. As may be appreciated, anincrease in the piston cross-sectional area of an actuator correspondsto an increase in the size and weight of the hydraulic system componentsincluding the size and weight of the actuators, tubing, reservoirs, andother components. The increased size of the actuators may protrudefurther outside of the outer mold line of the aerodynamic surfacesresulting in an increase in aerodynamic drag of an aircraft. The reducedattitude controllability, increased weight of the hydraulic system, andincreased aerodynamic drag may reduce safety, fuel efficiency, range,and/or payload capacity of the aircraft.

As can be seen, there exists a need in the art for a system and methodfor allowing the operating bandwidth of an actuator to match orencompass the resonant frequency of a movable device without oscillatoryresponse.

In addition, flutter suppression is a known challenge for high-pressure,hydraulic, flight-control actuation. High pressure hydraulics systemsface an upper limit due to aero-servo-elasticity which drives a lowerlimit on actuator linear stiffness. That lower limit depends on thekinematics and inertia of the flight control surface.

Known flight control systems and method for addressing fluttersuppression are primarily focused on increasing linear stiffness byincreasing actuator piston diameter, which may cause increased flightcontrol system and aircraft size, weight, and power. Increased flightcontrol system and aircraft size, weight, and power may result inincreased flight fuel costs. Other known flight control systems andmethods for addressing flutter suppression attempt to enhance the activecontrol system performance by increasing the servo bandwidth to operatein the high dynamic resonant frequency range of the actuator and valve.However, such known flight control systems and methods involve the usedof active control elements, such as the actuator and valve size ordiameter, rather than a passive means to change the dynamics of theflight control system. The use of such active control elements mayoverly complicate the control elements, be less space efficient, and maybe unreliable.

As can be seen, there exists a need in the art for an assembly andmethod to address flutter suppression and flutter critical controlsurface applications on aircraft, to dampen movement of flight controlsurfaces, and to optimize a flight control system design in terms ofimproved reliability, space efficiency and changing the dynamiccharacteristics of the hardware under control rather than complicatingthe flight control system elements themselves.

SUMMARY

The above-noted needs associated with actuators are specificallyaddressed and alleviated by the present disclosure which provides a dualrack and pinion rotational inerter system for damping movement of aflight control surface of an aircraft. The dual rack and pinionrotational inerter system comprises a flexible holding structuredisposed between the flight control surface and a support structure ofthe aircraft.

The system further comprises a dual rack and pinion assembly held by andbetween the flexible holding structure. The dual rack and pinionassembly comprises a first rack, a second rack, and a pinion engaged toand between the first rack and the second rack. The system furthercomprises a first terminal coupled to the first rack and coupled to theflight control surface, via a pivot element, and a second terminalcoupled to the second rack, and coupled to the support structure.

The system further comprises a pair of inertia wheels comprising a firstinertia wheel adjacent to a first side of the flexible holdingstructure, and a second inertial wheel adjacent to a second side of theflexible holding structure. The system further comprises an axle elementinserted through the first inertial wheel, the flexible holdingstructure, the pinion, and the second inertial wheel, coupling arotational movement of the pair of inertia wheels and the pinion.

Rotation of the flight control surface causes translational movement,via the pivot element, of the first rack relative to the second rack,along a longitudinal inerter axis, which causes the rotational movementof the pinion and the pair of inertia wheels, such that the rotationalmovement of the pinion is resisted by the pair of inertia wheels,resulting in the dual rack and pinion rotational inerter system dampingmovement of the flight control surface.

Also disclosed is an aircraft comprising a flight control surfacepivotably coupled to a support structure, one or more actuatorsconfigured to actuate the flight control surface, and at least one dualrack and pinion rotational inerter system for damping movement of theflight control surface of the aircraft.

The dual rack and pinion rotational inerter system comprises a flexibleholding structure disposed between the flight control surface and thesupport structure of the aircraft. The dual rack and pinion rotationalinerter system further comprises a plurality of rod bearings insertedinto interior corners of the flexible holding structure. The dual rackand pinion rotational inerter system further comprises a dual rack andpinion assembly clamped by and between the flexible holding structure.The dual rack and pinion assembly comprises a first rack, a second rack,and a pinion engaged to and between the first rack and the second rack.

The dual rack and pinion rotational inerter system further comprises afirst terminal coupled to the first rack and coupled to the flightcontrol surface, via a pivot element, and a second terminal coupled tothe second rack, and coupled to the support structure. The dual rack andpinion rotational inerter system further comprises a pair of inertiawheels comprising a first inertia wheel adjacent to a first side of theflexible holding structure, and a second inertial wheel adjacent to asecond side of the flexible holding structure. The dual rack and pinionrotational inerter system further comprises an axle element insertedthrough the first inertial wheel, the flexible holding structure, thepinion, and the second inertial wheel, coupling a rotational movement ofthe pair of inertia wheels and the pinion.

Rotation of the flight control surface causes translational movement,via the pivot element, of the first rack relative to the second rack,along a longitudinal inerter axis, which causes the rotational movementof the pinion and the pair of inertia wheels, such that the rotationalmovement of the pinion is resisted by the pair of inertia wheels. Thisresults in the dual rack and pinion rotational inerter system dampingmovement of the flight control surface.

Also disclosed is a method for damping movement of a flight controlsurface of an aircraft. The method comprises the step of installing atleast one dual rack and pinion rotational inerter system between theflight control surface and a support structure of the aircraft.

The dual rack and pinion rotational inerter system comprises a flexibleholding structure having a plurality of rod bearings inserted intointerior corners of the flexible holding structure. The dual rack andpinion rotational inerter system further comprises a dual rack andpinion assembly clamped by and between the flexible holding structure.The dual rack and pinion assembly comprises a first rack, a second rack,and a pinion engaged to and between the first rack and the second rack.

The dual rack and pinion rotational inerter system further comprises afirst terminal coupled to the first rack and coupled to the flightcontrol surface, via a pivot element, and a second terminal coupled tothe second rack, and coupled to the support structure. The dual rack andpinion rotational inerter system further comprises a pair of inertiawheels comprising a first inertia wheel adjacent to a first side of theflexible holding structure, and a second inertial wheel adjacent to asecond side of the flexible holding structure. The dual rack and pinionrotational inerter system further comprises an axle element insertedthrough the first inertial wheel, the flexible holding structure, thepinion, and the second inertial wheel, and the axle element coupling arotational movement of the pair of inertia wheels and the pinion.

The method further comprises the step of rotating the flight controlsurface using one or more actuators. The method further comprises thestep of using the at least one dual rack and pinion rotational inerterto axially accelerate and pull in a translational movement along alongitudinal inerter axis, the first rack relative to the second rack,and to cause the rotational movement of the pinion and the pair ofinertia wheels, such that the rotational movement of the pinion isresisted by the pair of inertia wheels and there is no incidentalmotion. The method further comprises the step of damping movement of theflight control surface, using the at least one dual rack and pinionrotational inerter.

The above-noted needs associated with actuators are specificallyaddressed and alleviated by the present disclosure which provides anapparatus including an inerter for damping an actuator. The inerterincludes a first terminal and a second terminal movable relative to oneanother along an inerter axis and configured to be mutually exclusivelycoupled to a support structure and a movable device actuated by anactuator. In one example, the inerter further includes a rod coupled toand movable with the first terminal. The inerter also includes athreaded shaft coupled to and movable with the second terminal. Theinerter additionally includes a flywheel having a flywheel annuluscoupled to the rod. The flywheel is configured to rotate in proportionto axial acceleration of the rod relative to the threaded shaft incorrespondence with actuation of the movable device by the actuator.

Also disclosed is aircraft having a flight control surface pivotablycoupled to a support structure of the aircraft. The aircraft furtherincludes a hydraulic actuator configured to actuate the flight controlsurface. In addition, the aircraft includes an inerter having a firstterminal and a second terminal mutually exclusively coupled to thesupport structure and the flight control surface. The inerteradditionally includes a rod movable with the first terminal, and athreaded shaft movable with the second terminal. The inerter alsoincludes a flywheel coupled to the rod and the threaded shaft. Theflywheel is configured to rotate in proportion to axial acceleration ofthe rod relative to the threaded shaft in correspondence with actuationof the flight control surface by the actuator.

In addition, disclosed is a method of damping an actuator. The methodincludes actuating, using an actuator, a movable device. In addition,the method includes axially accelerating, using an inerter coupled tothe movable device, a first terminal relative to a second terminal ofthe inerter simultaneous with and in proportion to actuation of themovable device. Furthermore, the method includes rotationallyaccelerating a flywheel of the inerter in proportion to and simultaneouswith the axial acceleration of the first terminal relative to the secondterminal. Additionally, the method includes reducing actuator loadoscillatory amplitude of the movable device and actuator in response torotationally accelerating the flywheel.

The features, functions and advantages that have been discussed can beachieved independently in various examples of the present disclosure ormay be combined in yet other examples, further details of which can beseen with reference to the following description and drawings below.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of the present disclosure will become moreapparent upon reference to the drawings wherein like numbers refer tolike parts throughout and wherein:

FIG. 1 is a block diagram of a flight control system of an aircraftincluding a hydraulic actuator for actuating a flight control surfaceand further including an inerter for damping the hydraulic actuator;

FIG. 2 is a block diagram of an example of an inerter integrated into ahydraulic actuator;

FIG. 3 is a perspective view of an aircraft;

FIG. 4 is a top view of a portion of a wing illustrating an actuator andan inerter operatively coupled to an aileron;

FIG. 5 is a sectional view of a wing taken along line 5 of FIG. 4 andillustrating an example of a linear hydraulic actuator mechanicallycoupled between a wing spar and one end of an aileron;

FIG. 6 is a sectional view of the wing taken along line 6 of FIG. 4 andillustrating an example of an inerter coupled to the aileron on an endopposite the actuator;

FIG. 7 is a sectional view of an example of a linear hydraulic actuatorhaving a piston axially slidable within an actuator housing;

FIG. 8 is a sectional view of an example of an inerter having a rodcoupled to a first terminal and a threaded shaft coupled to a secondterminal and including a flywheel threadably engaged to the threadedshaft and configured to rotate in proportion to axial acceleration ofthe rod and first terminal relative to the threaded shaft and secondterminal;

FIG. 9 is a magnified sectional view of the flywheel taken along line 9of FIG. 8 and illustrating a bearing rotatably coupling the flywheelannulus to the inerter rod and further illustrating the threadableengagement of the flywheel to the threaded shaft;

FIG. 10 is a sectional view of an example of an inerter integrated intoan unbalanced hydraulic actuator and illustrating the inerter flywheelrotatably coupled to a piston of the hydraulic actuator;

FIG. 11 is a sectional view of an example of an inerter having flywheelprotrusions for generating viscous damping within hydraulic fluid duringrotation of the flywheel;

FIG. 12 is a perspective view of an example of an inerter taken alongline 12 of FIG. 11 and illustrating a plurality of radially extendingflywheel blades circumferentially spaced around the flywheel perimeter;

FIG. 13 is a sectional view of an example of an inerter integrated intoa partially-balanced hydraulic actuator having an interior pistonaxially slidable within the piston rod;

FIG. 14 is a sectional view of an example of an inerter integrated intoa balanced hydraulic actuator having opposing piston sides withsubstantially equivalent cross-sectional areas;

FIG. 15 is a sectional view of an example of an inerter integrated intoa hydraulic actuator and wherein the flywheel is rotatably housed withinthe piston of the hydraulic actuator and including an electric flywheelmotor and a brake for actively controlling rotation of the flywheel;

FIG. 16 is a magnified sectional view of the flywheel and piston takenalong line 16 of FIG. 15 and illustrating the electric flywheel motorhaving permanent magnets mounted to the flywheel perimeter and windingsmounted to the piston inner wall;

FIG. 17 is a sectional view of an example of an inerter integrated intoa hydraulic actuator and wherein the flywheel and threaded shaft arerotatably coupled to the actuator end wall and the piston fixedlycoupled to the rod;

FIG. 18 is a magnified sectional view of the flywheel and piston takenalong line 18 of FIG. 17 and illustrating the flywheel annulus rotatablycoupled to the actuator end wall and the piston threadably engaged tothe threaded shaft in a manner such that linear translation of the rodrelative to the threaded shaft causes rotation of the flywheel andthreaded shaft;

FIG. 19 is a sectional view of an example of a flywheel rotatablycoupled to the actuator end wall and having an electric flywheel motorincluding permanent magnets mounted to the flywheel perimeter andwindings mounted to the housing side wall of the actuator;

FIG. 20 is a sectional view of a further example of a flywheel having anelectric flywheel motor and further including a brake configured toprovide dynamic braking of the flywheel;

FIG. 21 is a sectional view of an example of an inerter integrated intoa linear electro-mechanical actuator and illustrating the flywheelrotatably coupled to an actuator motor and threadably engaged to athreaded shaft;

FIG. 22 is a sectional view of an example of an inerter integrated intoa hydraulic actuator and illustrating the notations x, x₀, x₁, and x₂respectively denoting reference points for translation of the rod end,the cap end, the piston, and the flywheel wherein the notations are usedin the derivation of a transfer function characterizing the response ofan actuator having an integrated inerter;

FIG. 23 is a graph plotting frequency vs. magnitude (e.g., amplitude)for an actuator operating under a working pressure of 3000 psi, 5000psi, and 8000 psi, and illustrating a reduction in amplitude for theactuator damped by an inerter relative to the amplitude of the actuatorundamped by an inerter;

FIG. 24 is a flowchart having one or more operations that may beincluded in method of damping an actuator using an inerter;

FIG. 25 is a perspective view of an aircraft;

FIG. 26 is a top view of a wing section of a wing, taken along line26-26 of FIG. 25, illustrating an actuator and a dual rack and pinionrotational inerter system operatively coupled between a flight controlsurface and a support structure;

FIG. 27 is a sectional view of the wing section, taken along line 27-27of FIG. 26, and illustrating an example of a dual rack and pinionrotational inerter system installed between the flight control surfaceand the support structure;

FIG. 28 is a sectional view of the wing section, taken along line 28-28of FIG. 26, and illustrating an example of a hydraulic actuatormechanically coupled between a wing spar and one end of an aileron;

FIG. 29A is an exploded perspective view of an example of a dual rackand pinion rotational inerter system of the disclosure in a disassembledposition;

FIG. 29B is a perspective view of the dual rack and pinion rotationalinerter system of FIG. 29A in an assembled position;

FIG. 29C is a cross-sectional view of the dual rack and pinionrotational inerter system of FIG. 29B, taken along lines 29C-29C of FIG.29B;

FIG. 30 is a block diagram of a flight control system of an aircraftincluding one or more actuators for actuating a flight control surface,and further including a dual rack and pinion rotational inerter systemfor damping movement of the flight control surface; and

FIG. 31 is a flowchart having one or more operations that may beincluded in a method for damping movement of a flight control surface ofan aircraft.

DETAILED DESCRIPTION

Referring now to the drawings wherein the showings are for purposes ofillustrating various examples of the present disclosure, shown in FIG. 1is a block diagram of a hydraulic actuator 204 coupled between a supportstructure 116 and a movable device 124 and configured to move or actuatethe movable device 124. The block diagram advantageously includes arotational inerter 300 for damping the actuator 202. The inerter 300 isshown coupled between the support structure 116 and the movable device124 and is configured to improve the dynamic response of the movabledevice 124 during actuation by the actuator 202, as described in greaterdetail below. In the example shown in FIGS. 1 and 4-9, the inerter 300is provided as a separate component from the actuator 202. However, inother examples (e.g., FIGS. 2 and 10-21) described below, the inerter300 is integrated into the actuator 202.

The actuator 202 includes a piston 216 coupled to a piston rod 224. Thepiston 216 is slidable within an actuator housing 228 (e.g., acylinder). The actuator 202 further includes a rod end 214 and a cap end212 axially movable relative to one another in response to pressurizedhydraulic fluid acting in an unbalanced manner on one or both sides ofthe piston 216 inside the actuator housing 228. In the example shown,the rod end 214 is coupled to the movable device 124 and the cap end 212is coupled to the support structure 116. However, the actuator 202 maybe mounted such that the rod end 214 is coupled to the support structure116 and the cap end 212 is coupled to the movable device 124.

Referring still to FIG. 1, the inerter 300 includes a first terminal 302and a second terminal 304 axially movable or translatable relative toone another along an inerter axis 306 (FIG. 8) in correspondence withactuation of the movable device 124 by the actuator 202. In the exampleshown, the first terminal 302 is coupled to the movable device 124 andthe second terminal 304 is coupled to the support structure 116.However, the inerter 300 may be mounted such that the first terminal 302is coupled to the support structure 116 and the second terminal 304 iscoupled to the movable device 124. In an example not shown, the supportstructure to which the inerter 300 is coupled may be a different supportstructure than the support structure 116 to which the actuator 202 iscoupled.

The inerter 300 includes an inerter rod 308 coupled to and axiallymovable (e.g., translatable) with the first terminal 302. The inerterrod 308 may be aligned with or parallel to the inerter axis 306. Theinerter rod 308 may be hollow to define a rod bore 310. The threadedshaft 322 is coupled to and axially movable (e.g., translatable) withthe second terminal 304. The threaded shaft 322 may be aligned with orparallel to the inerter axis 306. The threaded shaft 322 has a free end324 that may be receivable within the rod bore 310. The threaded shaft322 may be hollow or may include a shaft bore 323 open on the free end324 of the threaded shaft 322. The threaded shaft 322 may include radialpassages 325 extending radially from the shaft bore 323 to the exteriorside of the threaded shaft 322 to allow fluid flow between the exteriorside of the threaded shaft 322 and the shaft bore 323. The shaft bore323 may allow fluid (e.g., hydraulic fluid—not shown) to flow from thefluid cavity at a second terminal 304 (for non-integratedinerters—FIG. 1) or cap end 212 (for integrated inerters—FIG. 2),through the shaft bore 323, and into the fluid cavity at the free end324 (FIG. 8) of the threaded shaft 322 to allow the fluid to lubricatemoving parts of the hearing 328 and/or at the flywheel annulus 318. Thesize (e.g., diameter) of the shaft bore 323 and the size (e.g.,diameter) and quantity of the radial passages 325 may be configured toapportion fluid flow to the bearing 328 and the flywheel annulus 318.

As shown in FIG. 1, the inerter 300 includes a flywheel 314 (e.g., aspinning mass). In some examples (e.g., FIGS. 6 and 8-16), the flywheel314 is threadably coupled to the threaded shaft 322 which convertslinear motion of the threaded shaft 322 into rotational motion of theflywheel 314. The flywheel 314 is configured to rotate in proportion toaxial movement of the inerter rod 308 relative to the threaded shaft 322in correspondence with actuation of the movable device 124 by theactuator 202. In this regard, the flywheel 314 is configured torotationally accelerate and decelerate in proportion to axialacceleration and deceleration of the inerter rod 308 (e.g., coupled tothe first terminal 302) relative to the threaded shaft 322 (e.g.,coupled to the second terminal 304).

Advantageously, the flywheel 314 is coupled to the inerter rod 308 at aflywheel annulus 318 and is threadably engaged to the threaded shaft322, as shown in FIGS. 1, 8-9, and 14 and described in greater detailbelow. However, in other examples, the flywheel annulus 318 may becoupled to the piston 216 as shown in FIGS. 10-13 and 15-16 anddescribed below. In still further examples, the flywheel annulus 318 maybe coupled to the actuator housing 228 as shown in FIGS. 17-20 anddescribed below.

Regardless of the component to which the flywheel 314 is coupled, theflywheel 314 may include at least one bearing 328 (e.g., a thrustbearing 328) at the flywheel annulus 318 to rotatably couple theflywheel 314 to the inerter rod 308 (FIGS. 1, 8-9, and 14), the piston216 (FIGS. 10-13 and 15-16), or the actuator housing 228 (FIGS. 17-20).The bearing 328 allows the flywheel 314 to axially translate with theinerter rod 308 as the flywheel 314 rotates on the threads of thethreaded shaft 322 in response to axial movement of the inerter rod 308relative to the threaded shaft 322. Advantageously, by coupling theflywheel 314 to the component (i.e., the inerter rod 308, the piston216, or the actuator housing 228) at the flywheel annulus 318 instead ofat the flywheel perimeter 316, the flywheel 314 exhibits limited flexurein the axial direction during high-frequency, oscillatory, axialacceleration of the first terminal 302 relative to the second terminal304. Such axial flexure of the flywheel mass would otherwise reduceflywheel rotational motion during high-frequency, oscillatory, axialacceleration.

Referring still to the example of FIG. 1, the support structure 116 isshown configured as a spar 118 of a wing 114 of an aircraft 100. Themovable device 124 is shown as a flight control surface 122 of a flightcontrol system 120 of the aircraft 100. The flight control surface 122may be hingedly coupled to the rigid support structure 116 such as awing spar 118 or other structure. The flight control surface 122 may bepivotably about a hinge axis 126. The flight control surface 122 maycomprise any one of a variety of different configurations including, butnot limited to, a spoiler, an aileron, an elevator 112, an elevon, aflaperon, a rudder 108, a high-lift device such as a leading edge slat,a trailing edge flap, or any other type of movable device 124.

The actuator 202 provides positive force to move the flight controlsurface 122 to a commanded position in response to a command input fromthe flight crew or an autopilot. The inerter 300 provides for controland damping of displacements of the flight control surface 122. One ormore inerters 300 may be included in a flight control system 120. In oneexample, the one or more inerters 300 may be configured to suppress orprevent control surface flutter as may be aerodynamically-induced at aresonant frequency of the flight control surface 122. For example, thepresently-disclosed inerter 300 may be configured to reduce actuatorload oscillatory amplitude at resonance (e.g., at a resonant frequency)of up to approximately 20 Hz (e.g., ±5 Hz) which may correspond to theflutter frequency of a flight control surface 122 of an aircraft 100.Additionally or alternatively, the inerter 300 may provide additionalfunctionality for improving the dynamic response of a movable device124, such as increasing the actuation rate of the movable device 124and/or preventing position overshoot of a commanded position of themovable device 124, as described in greater detail below.

In one example, the inerter 300 may be configured such that rotation ofthe flywheel 314 reduces actuator load oscillatory amplitude atresonance of the coupled actuator 202 and movable device 124 by at leastapproximately 10 percent relative to the actuator load oscillatoryamplitude that would otherwise occur using the same actuator 202 withoutan inerter 300. Advantageously, the presently-disclosed inerter 300permits the operating bandwidth of the actuator 202 to encompass ormatch the resonant frequency of the coupled movable device 124 andactuator 202 without the potential for oscillatory response, without thepotential for exceeding the strength capability of the mounting system(not shown) of the flight control surface 122 and actuator 202, and/orwithout the potential for flight control surface 122 deflections thatcould aerodynamically destabilize the aircraft 100.

The presently-disclosed examples of the inerter 300 allow for areduction in the overall size and weight of an actuator 202 systemwithout the potential for oscillatory response. More specifically, theinerter 300 allows for a reduction in the inertial load on the actuator202 which, in turn, allows for a reduction in piston cross-sectionalarea of the actuator 202 and a decrease in the size and weight of otherhydraulic system components including reservoirs, tubing diameter,accumulators, pumps, and other components. In this regard, the inerter300 increases the power density for a hydraulic actuator system in anyapplication where dynamic response is limited by piston cross-sectionalarea or load inertia. The presently-disclosed inerter 300 examples maybe implemented with hydraulic actuators 204 configured to be operated ata working pressure of at least 5000 psi. For example, the inerter 300examples may be implemented with hydraulic actuators 204 operated at aworking pressure of approximately 3000 psi and, in some examples, thehydraulic actuators 204 may be operated at a working pressure ofapproximately 8000 psi. A relatively high working pressure of ahydraulic actuator 204 may facilitate a reduction in total flow ofhydraulic fluid through the hydraulic system (e.g., flight controlsystem 120) which may enable a reduction in the volumetric requirementfor hydraulic fluid reservoirs and accumulators.

In the case of an aircraft 100, the reduced size of the actuators 202may reduce the amount by which such actuators 202 protrude outside ofthe outer mold line (not shown) of the aircraft 100 with a resultingdecrease in aerodynamic drag. Even further, the presently-disclosedinerter examples may allow for a reduction in the amount of off-takepower from the aircraft propulsion units (e.g., gas-turbine engines)which may provide the potential for using higher bypass ratio gasturbine engines such as in commercial aircraft applications. Thedecrease in the size of the hydraulic system, the reduction inaerodynamic drag, and/or the reduction in off-take power may translateto an increase in aircraft performance including, but not limited to,increased fuel efficiency, range, and/or payload capacity.

Although the presently-disclosed inerter examples are described in thecontext of a linear hydraulic actuator 204, the inerter 300 may beimplemented in other types of actuators 202 including, but not limitedto, a rotary hydraulic actuator, an electro-hydraulic actuator (e.g.,rotary or linear), a mechanical actuator, an electro-mechanicalactuator, and other types of actuators. In one example (see FIG. 21),the electro-mechanical actuator 242 may be a linear electro-mechanicalactuator having a threaded shaft 322 coupled to a movable device 124. Asdescribed in greater detail below with reference to FIG. 21, the linearelectro-mechanical actuator 242 may include an electric actuator motor244 for causing axial motion of a threaded shaft 322. A flywheel 314 maybe threadably engaged to the threaded shaft 322 and may be configured torotationally accelerate and decelerate in proportion to axialacceleration and deceleration of the threaded shaft 322 during actuationof the movable device 124 by the linear electro-mechanical actuator 242.

It should also be noted that although the presently-disclosed inerterexamples are described in the context of an aircraft flight controlsystem 120, any one of the inerters 300 may be implemented in any typeof open-loop or closed-loop control system for use in any one of avariety of different applications in any industry, without limitation.In this regard, the presently-disclosed inerters 300 may be implementedin any vehicular application or non-vehicular application. For example,an inerter 300 may be implemented in any marine, ground, air, and/orspace application, and in any vehicular or non-vehicular system,subsystem, assembly, subassembly, structure, building, machine, andapplication that uses an actuator to actuate a movable device.

In some examples, an inerter 300 may be implemented for damping movementof a movable device configured to control the direction of travel of avehicle. For example, an inerter may be implemented for damping movementof aerodynamic control surfaces of an air vehicle, hydrodynamic controlsurfaces of a marine vessel, thrust directors including thrust-vectoringnozzles of an aircraft or a launch vehicle (e.g., a rocket), or anyother type of mechanical device that influences the direction of travelof a vehicle and which may be susceptible to external vibratory forces.In a specific example of a wheeled vehicle configured to move over land,any one of the presently-disclosed inerter examples may be implementedin a steering system to control or avoid wheel shimmy, such as may occurin a steerable wheel of an aircraft landing gear such as a nose landinggear.

FIG. 2 is a block diagram of an example of an inerter 300 integratedinto a hydraulic actuator 204 coupled between a support structure 116and a flight control surface 122 of a flight control system 120 of anaircraft 100. In the example shown, the actuator 202 is a linearhydraulic actuator 204 having a piston 216 coupled to a rod (e.g.,piston rod 224) and axially slidable within a housing (not shown). Inthe example shown, the flywheel 314 of the inerter 300 is rotatablycoupled to the piston 216 at the flywheel annulus 318. The flywheel 314is threadably coupled to the threaded shaft 322 and configured torotationally accelerate in proportion to axial acceleration of thepiston 216 and rod relative to the threaded shaft 322. However, asmentioned above, the flywheel 314 may be rotatably coupled to the piston216 (e.g., FIGS. 10-16) or the flywheel 314 may be rotatably coupled tothe cap end 212 (e.g., FIGS. 17-20) or rod end 214 of the actuatorhousing 228.

As mentioned above, the threaded shaft 322 may include a shaft bore 323open on the free end 324 and having radial passages 325 to allow fluid(e.g., hydraulic fluid) to flow from the cap end chamber 236 at the capend 212), through the shaft bore 323, and out of the free end 324 of thethreaded shaft 322 to allow the fluid to lubricate moving parts of thebearing 328 and/or the flywheel annulus 318. The shaft bore 323 andradial passages 325 may be included in any one of the inerter 300examples disclosed herein.

In the present disclosure, for examples wherein the inerter 300 isintegrated into the actuator 202, the rod end 214 or cap end 212 of theactuator 202 functions as the first terminal 302 of the inerter 300, andthe remaining rod end 214 or cap end 212 of the actuator 202 functionsas the second terminal 304 of the inerter 300. In this regard, the terms“first terminal” and “second terminal” are non-respectively usedinterchangeably with the terms “rod end” and “cap end.” In addition, forexamples where the inerter 300 is integrated into the actuator 202, theterm “rod” is used interchangeably with the terms “piston rod” and“inerter rod.” Similarly, for examples where the inerter 300 isintegrated into the actuator 202, the term “housing” is usedinterchangeably with the terms “actuator housing” and “inerter housing.”

FIG. 3 is a perspective view of an aircraft 100 having one or moreinerters 300 for control and/or damping of one or more actuators 202.The aircraft 100 may include a fuselage 102 and a pair of wings 114extending outwardly from the fuselage 102. The aircraft 100 may includea pair of propulsion units (e.g., gas turbine engines). As mentionedabove, each wing 114 may include one or more movable devices 124configured as flight control surfaces 122 which may be actuated by anactuator 202 damped and/or assisted by an inerter 300. Such flightcontrol surfaces 122 on the wings 114 may include, but are not limitedto, spoilers, ailerons, and one or more high-lift devices such as aleading edge slats and/or trailing edge flaps. At the aft end of thefuselage 102, the empennage 104 may include one or more horizontal tails110 and a vertical tail 106, any one or more of which may include flightcontrol surfaces 122 such as an elevator 112, a rudder 108, or othertypes of movable devices 124 that may be actuated by an actuator 202damped and/or assisted by an inerter 300.

FIG. 4 is a top view of a portion of the wing 114 of FIG. 3 illustratingan aileron actuated by a hydraulic actuator 204 located on one end ofthe aileron and having an inerter 300 located on an opposite and theaileron 130. The aileron 130 may be hingedly coupled to a fixed supportstructure 116 of the wing 114 such as a spar 118. In FIG. 4, thehydraulic actuator 204 and the inerter 300 are provided as separatecomponents and may each be coupled between the support structure 116(e.g., the spar 118) and the aileron 130.

FIG. 5 is a sectional view of the wing 114 of FIG. 4 showing an exampleof a linear hydraulic actuator 204 mechanically coupled between the wingspar 118 and one end of the aileron 130. In the example shown, the rodend 214 of the hydraulic actuator 204 is coupled to a bellcrank 128. Thebellcrank 128 is hingedly coupled to the aileron in a manner such thatlinear actuation of the hydraulic actuator 204 causes pivoting of theaileron about the hinge axis 126. The cap end 212 of the hydraulicactuator 204 is coupled to the wing spar 118.

FIG. 6 is a sectional view of the wing 114 of FIG. 4 and showing anexample of an inerter 300 coupled between the wing spar 118 and theaileron 130. As mentioned above, the inerter 300 is located on an end ofthe aileron opposite the hydraulic actuator 204. The first terminal 302of the inerter 300 is coupled to a bellcrank 128. The second terminal304 of the inerter 300 is coupled to the wing spar 118. Due to thehydraulic actuator 204 and the inerter 300 being coupled to the samemovable device 124 (i.e., the aileron 130), relative axial accelerationof the cap end 212 and rod end 214 of the actuator 202 causesproportional axial acceleration of the first terminal 302 and secondterminal 304 of the inerter 300 resulting in rotational acceleration ofthe flywheel 314.

FIG. 7 is a partially cutaway sectional view of an example of adouble-acting hydraulic actuator 204 having a cap end 212 and a rod end214 axially movable relative to one another during actuation of themovable device 124. As mentioned above, the rod end 214 and the cap end212 may be mutually exclusively coupled to the support structure 116 andthe movable device 124. For example, the rod end 214 may be coupled tothe support structure 116 and the cap end 212 may be coupled to themovable device 124, or the rod end 214 may be coupled to the movabledevice 124 and the cap end 212 may be coupled to the support structure116.

In FIG. 7, the piston 216 is coupled to a free end 324 of the piston rod224 and is axially slidable within the actuator housing 228. The piston216 divides the actuator housing 228 into a cap end chamber 236 and arod end chamber 238. The actuator housing 228 of the double-actinghydraulic actuator 204 includes a pair of fluid ports 234 through whichpressurized hydraulic fluid enters and leaves the cap end chamber 236and the rod end chamber 238 chambers for moving the piston 216 withinthe actuator housing 228. In any of the presently-disclosed examples,the hydraulic actuator 204 may also be configured as a single-actingactuator (not shown) wherein the actuator housing 228 contains a singlefluid port 234 for receiving pressurized hydraulic fluid in the actuatorhousing 228 as a means to move the piston 216 along one direction withinthe actuator housing 228, and optionally include a biasing member (e.g.,a spring—not shown) for moving the piston 216 in an opposite direction.

FIG. 8 is a partially cutaway sectional view of an example of an inerter300 having an inerter housing 330 containing the flywheel 314 and havingan inerter side wall 334 and opposing inerter end walls 332. One inerterend wall 332 may include a housing bore through which the inerter rod308 extends and terminates at the first terminal 302. The inerter 300includes a threaded shaft 322 coupled to the inerter end wall 332located at the second terminal 304. In the example of FIG. 8, theflywheel 314 is coupled to an end of the inerter rod 308 and threadablyengaged to the threaded shaft 322. The flywheel 314 rotates inproportion to axial acceleration of the inerter rod 308 and firstterminal 302 relative to the threaded shaft 322 and second terminal 304.

FIG. 9 is a magnified sectional view of FIG. 8 showing the flywheel 314coupled to the inerter rod 308 at the flywheel annulus 318. The flywheelannulus 318 is also threadably engaged to the threaded shaft 322. In theexample shown, the threaded shaft 322 is configured as a ball screw 326having helical grooves for receiving ball bearings which couplesimilarly-configured helical grooves in the flywheel annulus 318 to theball screw 326 with minimal friction. Although not shown, the flywheelannulus 318 may include a ball nut for circulating the ball bearingscoupling the flywheel 314 to the ball screw 326. In another example notshown, the threaded shaft 322 may comprise a lead screw having threadsto which the flywheel annulus 318 are directly engaged. As may beappreciated, the flywheel 314 may be configured for engagement to anyone of a variety of different types of configurations of threadedshafts, and is not limited to the ball screw 326 example illustrated inFIG. 9.

Also shown in FIG. 9 is an example of a bearing 328 for coupling theflywheel annulus 318 to the inerter rod 308 such that the inerter rod308 and flywheel 314 may translate in unison as the flywheel 314 rotatesdue to threadable engagement with the threaded shaft 322. Although thebearing 328 is shown as a ball bearing, the bearing 328 may be providedin any one a variety of different configurations capable of axiallycoupling the flywheel 314 to the inerter rod 308 with a minimal amountof axial free play. For example, the bearing 328 may be configured as aroller bearing (not shown). In still further examples, the flywheel 314may be coupled to the inerter rod 308 without a bearing while stillallowing the flywheel 314 to rotate during translation of the inerterrod 308 and flywheel 314 relative to the threaded shaft 322.

FIG. 10 is a sectional view of an example of an inerter 300 integratedinto a hydraulic actuator 204 having a housing containing a piston 216.The actuator 202 is a double-acting actuator including a pair of fluidports 234 for receiving pressurized hydraulic fluid in a cap end chamber236 and a rod end chamber 238 located on opposite sides of the piston216. The actuator 202 is an unbalanced actuator 206 wherein one of thepiston sides 218 has a greater cross-sectional area than the oppositepiston side 218. The piston 216 may include a piston 216 seal (e.g., anO-ring seal—not shown) extending around the piston perimeter 220 forsealing the piston perimeter 220 to the actuator side wall 232.

As mentioned above, for examples where the inerter 300 is integratedinto an actuator 202, the rod end 214 or the cap end 212 of the actuator202 functions as the first terminal 302 of the inerter 300, and theremaining rod end 214 or the cap end 212 of the actuator 202 functionsas the second terminal 304 of the inerter 300. In the example shown, theflywheel 314 is mounted in the cap end chamber 236 and is rotatablycoupled to the piston 216 at the flywheel annulus 318. The flywheel 314is threadably engaged to the threaded shaft 322 which passes through thepiston 216 and extends into the rod bore 310. The flywheel 314 isconfigured to rotationally accelerate in proportion to axialacceleration of the piston 216 and piston rod 224 relative to thethreaded shaft 322.

FIG. 11 shows an example of an inerter 300 having flywheel protrusions320 for generating viscous damping during rotation of the flywheel 314when the flywheel 314 is immersed in hydraulic fluid. The flywheelprotrusions 320 generate or increase the viscous damping capability ofthe inerter 300 during rotation of the flywheel 314, and therebyincrease the damping capability of the inerter 300.

FIG. 12 is a perspective view of an example of an inerter 300 having aplurality of radially extending flywheel blades circumferentially spacedaround the flywheel perimeter 316. During rotation of the flywheel 314,the flywheel blades may generate viscous damping capability and add tothe inerting capability of the inerter 300. Although FIG. 12 illustratesthe flywheel protrusions 320 as radially-extending flywheel blades, theflywheel 314 may be provided with flywheel protrusions 320 extendingfrom any portion of the flywheel 314 including one or both of theopposing sides of the flywheel 314. In addition, the flywheelprotrusions 320 may be provided in any geometric size, shape orconfiguration, without limitation, and are not limited to flywheelblades.

FIG. 13 is a sectional view of an example of an inerter 300 integratedinto a hydraulic actuator 204 configured as a partially-balancedactuator 208. The partially-balanced actuator 208 includes an interiorpiston 226 coupled to a free end 324 of the threaded shaft 322. Theinterior piston 226 may be axially slidable within the rod bore 310 andmay be rotatably coupled to the end of the threaded shaft 322 such thatthe interior piston 226 is non-rotatable relative to the rod bore 310during axial movement of the piston rod 224 relative to the threadedshaft 322. Although not shown, the perimeter of the interior piston 226may be sealed (e.g., via an O-ring) to the rod wall 312 of the rod bore310. The inclusion of the interior piston 226 may reduce the totalvolume of hydraulic fluid required to fill the cap end chamber 236during extension of the piston rod 224 relative to the increased volumeof hydraulic fluid required to fill the cap end chamber 236 for examples(e.g., FIG. 8) lacking an interior piston 226.

FIG. 14 is a partially cutaway sectional view of an example of aninerter 300 integrated into a hydraulic actuator 204 configured as abalanced actuator 210 having opposing piston sides 218 withsubstantially equivalent cross-sectional areas. The housing may includea separator wall 240 separating the portion of the housing containingthe flywheel 314 from the portion of the housing containing the piston216. A cap end chamber 236 is located on one of the piston sides 218 andthe rod end chamber 238 is located on the opposite piston side 218. Thepiston 216 may be mounted on the piston rod 224. In FIG. 14, one end ofthe piston rod 224 extends through the actuator end wall 230 andterminates at the rod end 214 (e.g., the first terminal 302). Anopposite end of the piston rod 224 extends through the separator wall240. The flywheel 314 is rotatably coupled to the piston rod 224 in amanner as described above.

FIG. 15 is a partially cutaway sectional view of an example of aninerter 300 having an electric flywheel motor 350 integrated into ahydraulic actuator 204. The flywheel motor 350 may facilitate activecontrol of flywheel 314 rotation using electromotive force from theintegrated flywheel motor 350. Active control may include using theflywheel motor 350 to apply a torque to the flywheel 314 to resist oraid the torque that is generated by the flywheel 314 due to axialacceleration of the first terminal 302 relative to the second terminal304. The flywheel motor 350 may be configured to provide active dampingand/or active braking of the actuator 202 and the load inertia.

FIG. 16 is a magnified sectional view of FIG. 15 showing the flywheel314 rotatably coupled to and contained within a generally hollow piston216 which is actually slidable within the actuator housing 230. Alsoshown in the flywheel motor 350 incorporated into the flywheel 314 andthe piston 216 and configured to actively control rotation of theflywheel 314 in correspondence with relative axial movement of the rodand threaded shaft 322. The flywheel motor 350 may be operated in amanner to accelerate and/or decelerate the flywheel 314 by applying atorque to the flywheel 314 either in correspondence with (e.g., the samedirection as) or in opposition to the direction of rotation of theflywheel 314. In this manner, the flywheel motor 350 may apply a torqueto the flywheel 314 to resist or aid the flywheel torque generated dueto axial acceleration of the first terminal 302 relative to the secondterminal 304.

In the example of FIG. 16, the flywheel motor 350 is a permanent magnetdirect-current (DC) motor having one or more permanent magnets 354mounted to the flywheel 314. For example, a plurality of permanentmagnets 354 may be circumferentially spaced around the flywheelperimeter 316. In addition, the flywheel motor 350 may include aplurality of windings 352 mounted to the piston 216. In one example, aplurality of windings 352 may be circumferentially spaced around thepiston inner wall 222 (e.g., FIGS. 15-16). In another example, aplurality of windings 352 may be circumferentially spaced around theside wall 232 of the housing (e.g., FIGS. 19-20) as described below. Inother examples, the flywheel motor 350 may be a brushless DC motor orsome other motor configuration, and is not limited to a permanent magnetDC motor configuration as shown in FIGS. 15-16 and 19-20. In an examplenot shown, a linear position sensor may be included with the actuator202 to sense the linear position of the piston 216 and generate a signalrepresentative of the linear piston position for commutating theflywheel motor 350 in correspondence with the piston position.

As mentioned above, the flywheel motor 350 in FIGS. 15-16 may beconfigured to assist or aid in rotating the flywheel 314 for a commandeddirection of motion of the movable device 124. For example, the flywheelmotor 350 may provide a torque to accelerate the flywheel 314 at thestart of motion of the movable device 124 toward a commanded position.The torque applied to the flywheel 314 by the flywheel motor 350 may beapproximately equal in magnitude to the torque required to rotationallyaccelerate the flywheel 314 due to axial acceleration of the threadedshaft 322 relative to the rod. By using the flywheel motor 350 to removethe torque required to rotationally accelerate the flywheel 314, thepiston 216 may move more quickly to a commanded position than if theflywheel motor 350 did not accelerate the flywheel 314. In this manner,the flywheel motor 350 may allow faster responsiveness of a movabledevice 124 than a conventional actuator 202. The level of dampingprovided by an inerter 300 having active control of the flywheel 314 maybe greater than the damping that is feasible in a closed-loop controlsystem without active control due to the risk of control systeminstability. Although FIGS. 15-16 illustrate a flywheel motor 350incorporated into an inerter 300 integrated with an actuator 202, aflywheel motor 350 may be incorporated into an inerter 300 that is aseparate component from the actuator 202 (e.g., FIGS. 4-8).

In a further example of active control, the flywheel motor 350 may beoperated in a manner to provide a torque to decelerate the flywheel 314as the movable device 124 approaches a commanded position. In thisregard, the flywheel motor 350 may be operated as a brake to oppose theflywheel torque generated by the axial deceleration of the threadedshaft 322 relative to the piston rod 224. Actively controlling flywheel314 rotation in this manner may prevent or limit position overshoot ofthe movable device 124 and thereby increase the stability of the movabledevice 124. In such an arrangement, the actuator 202 and inerter 300 maybe configured with a failure mode that ensures that without active motorcontrol, the actuator 202 is capable of exhibiting a desired dampedresponse in a manner preventing underdamping of the movable device 124.An inerter 300 having a flywheel motor 350 for active control may beconnected to the movable device 124 without being part of the actuator202 such that in the event of a disconnect of the actuator 202 from themovable device 124 or in the event of a failure of the actuator 202 tohold the load of the movable device 124, the flywheel motor 350 may beoperated in a manner preventing underdamped movement of the movabledevice 124 for the given failure mode.

Referring still to FIG. 16, in another example of active control, theflywheel motor 350 may include a brake 360 configured to provide dynamicbraking of the flywheel 314. In this regard, the brake 360 may beoperated in a manner to decelerate the flywheel 314 or to increaseexisting deceleration of the flywheel 314. For examples that include aflywheel motor 350, the brake 360 may be operated in a manner toincrease existing deceleration of the flywheel 314 caused by rotationaldrag of the flywheel motor 350. In addition, the flywheel motor 350 maybe operated in a manner to oppose disturbances (e.g., undesirablemotion) of the actuator 202.

In the example of FIG. 16, the brake 360 may be configured as a discbrake having brake pads 364. The flywheel 314 may function as a brakerotor against which the brake pads 364 may be frictionally engagedduring braking. In other examples not shown, a separate brake rotor maybe provided which may be directly or indirectly coupled to the flywheel314. In the example shown, a hydraulic brake cylinder (not shown) may beincluded to actuate the brake pads 364 into frictional engagement withone or both of the opposing axial faces 362 (e.g., planar faces) of theflywheel 314 for decelerating the flywheel 314. Preferably, the brake360 may include at least two pairs of opposing brake pads 364 located ondiametrically opposing sides of the brake rotor. Each pair of brake pads364 may be held in position by a bracket 366. Although the brake 360 isdescribed and illustrated as a disc brake, the inerter 300 mayincorporate any one or more different types of brakes such as a drumbrake or any other type of brake capable of decelerating the flywheel314.

Referring to FIG. 17, shown is a partially cutaway sectional view ofanother example of an inerter 300 integrated into a hydraulic actuator204. The flywheel 314 is rotatably coupled or attached to the actuatorend wall 230 which may be coupled to the second terminal 304. The piston216 is fixedly coupled or attached to the piston rod 224 which extendsfrom the piston 216 through the actuator end wall 230 and is coupled tothe first terminal 302. In an alternative example not shown, theflywheel 314 may be rotatably coupled to the actuator end wall 230 whichis attached to the first terminal 302, and the piston rod 224 may becoupled to the second terminal 304.

FIG. 18 is a magnified sectional view of FIG. 17 illustrating theflywheel annulus 318 rotatably coupled by a bearing 328 to the actuatorend wall 230. The threaded shaft 322 is fixedly coupled to the flywheel314 and is rotatable in unison with the flywheel 314. As mentionedabove, the piston 216 is fixedly coupled to the piston rod 224 andthreadably engaged to the threaded shaft 322 in a manner such thatlinear translation of the piston rod 224 relative to the threaded shaft322 causes rotation of the flywheel 314 and threaded shaft 322 inunison. As indicated above, axial movement of the threaded shaft 322relative to the piston rod 224 may be in correspondence with actuationof the movable device 124 by the actuator 202.

FIG. 19 illustrates an example of a flywheel 314 rotatably coupled tothe actuator end wall 230 and incorporating a flywheel motor 350 foractive control of the rotation of the flywheel 314 in a manner asdescribed above. The flywheel motor 350 may include permanent magnets354 mounted to the flywheel perimeter 316. For example, as describedabove with regard to FIG. 16, a plurality of permanent magnets 354 maybe circumferentially spaced around the flywheel perimeter 316. FIG. 19also shows a plurality of windings 352 circumferentially spaced aroundthe actuator side wall 232 of the actuator housing 228.

FIG. 20 illustrates an example of a flywheel 314 including a brake 360configured to provide dynamic braking of the flywheel 314. In theexample shown, the brake 360 is configured as a disc brake having one ormore pairs of brake pads 364 for frictionally engaging opposing axialfaces 362 of the flywheel 314. The brake 360 in FIG. 20 may beconfigured and operated similar to the arrangement illustrated in FIG.16 and described above.

FIG. 21 illustrates an example of an inerter 300 integrated into alinear electro-mechanical actuator 242. The electro-mechanical actuator242 may extend between a support structure 116 (FIG. 2) and a movabledevice 124 (FIG. 2). The electro-mechanical actuator 242 may include anelectric actuator motor 244 supported by the actuator housing 228. Thefirst terminal 302 may be coupled to a movable device 124. Theelectro-mechanical actuator 242 may include a second terminal 304 whichmay be coupled to a support structure 116. Alternatively, the firstterminal 302 may be coupled to the support structure 116 and the secondterminal 304 may be coupled to the movable device 124.

The electro-mechanical actuator 242 may include a threaded shaft 322(e.g., an Acme-threaded shaft, a ball screw, etc.) extending through theactuator motor 244 and terminating at the first terminal 302. Theactuator motor 244 may be operably coupled to the threaded shaft 322 bya motor-shaft coupler 246 which may be threadably engaged to thethreaded shaft 322. Operation of the actuator motor 244 may cause axialmotion of the threaded shaft 322 for actuating the movable device 124.In this regard, the threaded shaft 322 may axially move in proportion(e.g., in magnitude and direction) to angular displacement of theactuator motor 244. A flywheel 314 may be threadably engaged to thethreaded shaft 322. In addition, the flywheel annulus 318 may berotatably coupled to the actuator motor 244 via a bearing 328 such thataxial acceleration of the threaded shaft 322 causes rotationalacceleration of the flywheel 314. The flywheel 314 may be configured torotationally accelerate and decelerate in proportion to axialacceleration and deceleration of the threaded shaft 322 (e.g., relativeto the actuator motor 244) during actuation of the movable device 124.

In this regard, rotation of the flywheel 314 during actuation of theelectro-mechanical actuator 242 of FIG. 21 may provide any one or moreof the advantages described herein for improving the dynamic response ofthe movable device 124 during actuation by the electro-mechanicalactuator 242. For example, the flywheel 314 may reduce actuator loadoscillatory amplitude at resonance of the coupled electro-mechanicalactuator 242/movable device 124. In addition, although not shown in FIG.21, a flywheel motor 350 (e.g., FIG. 16) and/or a dynamic brake 360(FIG. 16) may optionally be included with the flywheel 314 to allow foractive control of the rotation of the flywheel 314 using any one or moreof the flywheel control techniques described herein.

FIG. 22 is a sectional view of an example of an inerter 300 integratedinto a hydraulic actuator 204 as described above and illustrated in FIG.10. FIG. 22 includes the notations x, x₀, x₁, and x₂ respectivelydenoting reference points for translation of the rod end 214, the capend 212, the piston 216, and the flywheel 314. The notations x, x₀, x₁,and x₂ are parameters that are used in a below-described derivation of atransfer function

$\frac{X(s)}{F(s)}$(Equation 220) mathematically characterizing the response of theapparatus of FIG. 22. Table 1 includes a listing of the parameters usedin the derivation of the transfer function. Included with each listedparameter is an indication of the physical type of the parameter and abrief description of the parameter.

TABLE 1 Parameter Physical type Description F force actuator reactedforce (newton) F₁ force piston reacted force (newton) F₂ force flywheelreacted force (newton) F₃ force flywheel to piston compliance force(newton) T₂ torque flywheel acceleration torque (newton-meter) {dot over(x)} translation actuator rod end translation reference (meter) x₁, {dotover (x)}₁, {umlaut over (x)}₁ translation piston translation reference(meter) x₂, {dot over (x)}₂, {umlaut over (x)}_(2,) translation flywheeltranslation transformed from rotation (meter) x₀, {dot over (x)}₀,{umlaut over (x)}₀ translation actuator cap end translation reference(meter) θ, {dot over (θ)}, {umlaut over (θ)} rotation flywheel rotationreference (radian) J mass moment of flywheel inertia in rotation(kilogram-meter²) inertia B damping coefficient flywheel torqueresisting {dot over (θ)} (newton-meter/radian/s) Z stiffness flywheelrotational stiffness (radian/newton-meter) M mass actuator reactedinertia at rod end (kilogram) C damping coefficient actuator forceresisting {dot over (x)} (newton/meter/s) K stiffness actuator stiffness(meter/newton) r thread rate revolutions per translation (radian/meter)ω_(n) natural frequency 2^(nd) order model characteristic(radian/second) ζ damping factor 2^(nd) order model characteristic (nounit) c constant zero offset to a common reference

Equations 100 to 210 inclusive are the assumptions behind the derivationof the transfer function of Equation 220. Referring to the exampleapparatus of FIG. 22, the total reacted force F (e.g., at the rod end214) may be computed as the sum of the piston 216 reacted force F₁ andthe flywheel 314 reacted force F₂ as shown in Equation 100, wherein thesign of F₁ and F₂ are the same from a disturbance rejection sense:F=F ₁ +F ₂  (Equation 100)

The torque T₂ developed by the flywheel 314 may be determined usingEquation 110 as the sum of the product of the flywheel rotationalinertia J and flywheel rotational acceleration {umlaut over (θ)} and theproduct of a flywheel damping coefficient B and the flywheel rotationalvelocity {dot over (θ)}:T ₂ =J{umlaut over (θ)}+B{dot over (θ)}  (Equation 110)

The flywheel reacted force F₂ may be computed using equation 120 as theproduct of the flywheel torque T₂ and the thread rate r (e.g., threadpitch) of the threaded shaft 322. The thread rate may be described asthe linear distance of travel of the flywheel 314 per revolution:F ₂ =r(J{umlaut over (θ)}+B{dot over (θ)})  (Equation 120)

The rotation of the flywheel 314 may be characterized by the flywheelangular displacement or rotational angle θ, rotational velocity {dotover (θ)}, and rotational acceleration {umlaut over (θ)}, asrespectively represented by Equations 130, 140, and 150. The flywheelrotational angle θ is the product of the thread rate r and the lineardistance of flywheel translation x₂ as represented by Equation 130. Theparameter c is a constant representing a linear offset relative to acommon reference. The flywheel rotational velocity {dot over (θ)} is theproduct of the thread rate r and the linear velocity {dot over (x)}₂ ofthe flywheel 314 as represented by Equation 140. The flywheel rotationalacceleration {dot over (θ)} is the product of the thread rate r and thelinear acceleration {umlaut over (x)}₂ of the flywheel 314 asrepresented by Equation 150.θ+c=rx ₂  (Equation 130){dot over (θ)}=r{dot over (x)} ₂  (Equation 140){umlaut over (θ)}=r{umlaut over (x)} ₂  (Equation 150)

A flywheel 314 to piston 216 compliance force F₃ may be computed usingEquation 160 as the product of the flywheel rotational stiffness Z andthe difference between flywheel translation x₂ and piston translationx₁. For the example apparatus of FIG. 22 wherein the inerter (e.g., theflywheel 314) is integrated into the actuator 202, the flywheel 314moves with the piston 216 such that the flywheel translation x₂ and thepiston translation x₁ are the same, as indicated below in Equation 190.In this regard, the piston compliance force F₃ is zero (0) due to theassumption that x₂=x₁ as indicated below in Equation 190.F ₃ =Z(x ₂ −x ₁)  (Equation 160)

Substituting Equations 140 and 150 for flywheel velocity {dot over (θ)}and flywheel acceleration {umlaut over (θ)} into Equation 120, theflywheel reacted force F₂ may be expressed as follows:F ₂ =r ²(J{umlaut over (x)} ₂ +B{dot over (x)}k ₂)  (Equation 170)

The piston reacted force F₁ may be computed as the sum of the product ofthe actuator (e.g., the piston) reacted inertia M at the rod end 214 andthe piston acceleration {umlaut over (x)}₁, the product of the actuator(e.g., the piston) resisting force C and the piston velocity {dot over(x)}, and the product of the actuator stiffness K and the pistondisplacement x₁, as shown in Equation 180:F ₁ =M{umlaut over (x)} ₁ +C{dot over (x)} ₁ +Kx ₁  (Equation 180)

As mentioned above, for the example shown in FIG. 22 wherein the inerter(e.g., the flywheel 314 and threaded shaft 322) is integrated into theactuator 202 such that the flywheel 314 and the piston 216 move inunison, the flywheel translation x₂ and the piston translation x₁ arethe same as represented by Equation 190. In addition the rod end 214 andthe piston 216 move in unison as represented by Equation 200. The capend 212 at x₀ is assumed to be fixed (e.g., non-translating) asrepresented by Equation 210.x ₂ =x ₁  (Equation 190){dot over (x)} ₁ ={dot over (x)}  (Equation 200){umlaut over (x)} ₀ ={dot over (x)} ₀ =x ₀=0  (Equation 210)

Performing a Laplace transform on a differential equation (not shown)representing the natural frequency of the example apparatus shown inFIG. 22, the resulting transfer function

$\frac{X(s)}{F(s)}$is expressed as shown in Equation 220 wherein X(s) represent theresponse of the apparatus of FIG. 22 and F(s) represents the input tothe apparatus:

$\begin{matrix}{\frac{X(s)}{F(s)} = \frac{\frac{1}{{r^{2}J} + M}}{s^{2} + {\frac{{r^{2}B} + C}{{r^{2}J} + M}s} + \frac{K}{{r^{2}J} + M}}} & \left( {{Equation}\mspace{14mu} 220} \right)\end{matrix}$

The natural frequency ω_(n) of oscillation of the example apparatus ofFIG. 22 may be expressed as shown in Equation 230 wherein K is theactuator stiffness, r is the thread rate, and J is the flywheelrotational inertia, as described above.

$\begin{matrix}{\omega_{n} = \left( \frac{K}{{r^{2}J} + M} \right)^{1/2}} & \left( {{Equation}\mspace{14mu} 230} \right)\end{matrix}$

Equation 240 represents the damping factor ζ of the example apparatus ofFIG. 22 which characterizes the decay in oscillatory response to theinput (e.g., flutter of a flight control surface).

$\begin{matrix}{\zeta = \frac{{r^{2}B} + C}{2\left( {K\left( {{r^{2}J} + M} \right)} \right)^{1/2}}} & \left( {{Equation}\mspace{14mu} 240} \right)\end{matrix}$

FIG. 23 is a graph plotting frequency 380 vs. magnitude 382 (amplitude)of the oscillatory response to a dynamic load for an actuator 202operating under three (3) different working pressures (3000 psi, 5000psi, and 8000 psi). The vertical centerline represents a flutterfrequency of 20 Hz corresponding to the dynamic load. The plots of FIG.23 illustrate the reduction in response amplitude 384 provided by theactuator 202 with integrated inerter 300 of FIG. 22, relative to theresponse amplitude for the same actuator operating without an inerter.The reduction in response amplitude represents an optimization based onsetting the response amplitude at the flutter frequency for the actuator202 operating at 8000 psi with an inerter 300 equal to the responseamplitude at the flutter frequency for the actuator 202 operating at3000 psi without the inerter 300, and optimizing the thread pitch r ofthe threaded shaft 322, the flywheel rotational inertia J, and thedamping factor ζ (Equation 240). For the actuator 202 operating at 8000psi, the inerter 300 facilitates a reduction in response amplitude 384of almost 5 dB at the flutter frequency of 20 Hz.

FIG. 24 is a flowchart having one or more operations that may beincluded in a method 400 of damping an actuator 202 using an inerter300. As mentioned above, the damping of the actuator 202 may comprisereducing actuator load oscillatory amplitude using inerter 300. Asindicated above, in some examples, the inerter 300 may be a separatecomponent from the actuator 202 and coupled to the same movable device124 as the actuator 202 (e.g., FIGS. 1 and 4-9). In other examples, theinerter 300 may be integrated into the actuator 202 (e.g., FIGS. 2 and10-22).

Step 402 of the method 400 includes actuating the movable device 124using an actuator 202. In the example of a flight control system 120 ofan aircraft 100, the method may include using a linear actuator such asa linear hydraulic actuator 204 or a linear electro-mechanical actuator242. For example, FIGS. 4-6 illustrate a linear hydraulic actuator 204configured to actuate an aileron 130 pivotably mounted to a wing 114 ofan aircraft 100. However, as mentioned above, the movable device 124 maybe any type of movable device that may be actuated by an actuator 202.

Step 404 of the method 400 includes axially accelerating, using aninerter 300 coupled to the movable device 124, the first terminal 302 ofthe inerter 300 relative to the second terminal 304 of the inerter 300.As indicated above, the inerter 300 may be coupled between the supportstructure 116 and the movable device 124 (e.g., FIGS. 4 and 6). Forexample, the first terminal 302 may be coupled to the movable device 124and the second terminal 304 may be coupled to the support structure 116,or the first terminal 302 may be coupled to the support structure 116and the second terminal 304 may be coupled to the movable device 124.Alternatively, the inerter 300 may be integrated into the actuator 202(e.g., FIGS. 10-21) which may be coupled between the support structure116 and the movable device 124. In such examples, as mentioned above,the rod end 214 or the cap end 212 of the actuator 202 functions as(e.g., is one and the same as) the first terminal 302 of the inerter300, and the remaining rod end 214 or cap end 212 of the actuator 202functions as (e.g., is one and the same as) the second terminal 304 ofthe inerter 300.

Step 406 of the method 400 includes rotationally accelerating theflywheel 314 simultaneous with the axial acceleration of the firstterminal 302 relative to the second terminal 304. Because the inerter300 and the actuator 202 are coupled to the same movable device 124(e.g., FIGS. 1 and 4-9) or because the inerter 300 is integrated intothe actuator 202 (e.g., FIGS. 2 and 10-21), the axial acceleration ofthe first terminal 302 relative to the second terminal 304 issimultaneous with and in proportion to the actuation of the movabledevice 124 by the actuator 202. In this regard, the flywheel 314rotationally accelerates and decelerates in proportion to the axialacceleration and deceleration of the first terminal 302 relative to thesecond terminal 304 in correspondence with the actuation of the movabledevice 124 by the actuator 202.

Step 408 of the method 400 includes damping the movement of the actuator202 in response to rotating the flywheel 314. In one example, the methodmay include reducing actuator load oscillatory amplitude of the movabledevice 124 in response to rotationally accelerating the flywheel 314.Regardless of whether the inerter 300 is a separate component from theactuator 202 or the inerter 300 is integrated into the actuator 202, themethod may include rotationally accelerating the flywheel 314 in amanner reducing actuator load oscillatory amplitude at resonance of themovable device 124 coupled to the actuator 202. In one example, themethod may include reducing actuator load oscillatory amplitude by atleast 50% relative to the oscillatory amplitude for the movable device124 actuated by the same actuator but without the inerter, as mentionedabove. The inerter 300 may be configured to reduce actuator loadoscillatory amplitude at a resonant frequency of up to approximately 20Hz (e.g., ±5 Hz). The movable device 124 may be a flight control surface122 (e.g., a hydraulically-actuated aileron 130) of an aircraft 100 andthe resonance (e.g., the resonant frequency) may correspond to flutterof the flight control surface 122 as induced by aerodynamic forcesacting on the flight control surface 122.

As mentioned above, in examples where the inerter 300 is integrated intothe actuator 202, the flywheel 314 may include a plurality of flywheelprotrusions 320 (e.g., flywheel blades—see FIGS. 11-12) extendingoutwardly from the flywheel 314. The flywheel 314 and the flywheelprotrusions 320 may be immersed in hydraulic fluid contained within thecap end chamber 236. In such examples, the method may include rotatingthe flywheel 314 within the hydraulic fluid and generating or increasingviscous damping of the actuator 202 movement in response to rotating theflywheel 314 in correspondence with the actuation of the movable device124. The viscous damping may contribute toward the damping provided bythe rotational inertia of the flywheel 314.

In still other examples, the method may include actively controlling therotation of the flywheel 314 in correspondence with relative axialmovement of the piston rod 224 and threaded shaft 322. For example, theinerter 300 may include or incorporate an electric flywheel motor 350 asdescribed above in the examples illustrated in FIGS. 15-16 and 19-20. Insome examples, as mentioned above, the actuator 202 may include a linearposition sensor (not shown) configured to sense the linear position ofthe piston 216 within the actuator 202 and generate a signalrepresentative of the piston position. The method may includecommutating the flywheel motor 350 in correspondence with the linearposition of the piston 216 as represented by the signal generated by theposition sensor.

Active control of the flywheel 314 rotation may include acceleratingand/or decelerating the flywheel 314 using the flywheel motor 350. Forexample, the flywheel motor 350 may be operated in a manner to apply atorque to the flywheel 314 in correspondence with or in the direction ofrotation of the flywheel 314. In this regard, the flywheel motor 350 mayassist a commanded direction of motion of the actuator 202. In someexamples, active control of flywheel rotation may include acceleratingthe flywheel 314 during initiation of actuation by the actuator 202 ofthe movable device 124 toward a commanded position. In this regard, theflywheel motor 350 may rotationally accelerate the flywheel 314 at thestart of axial acceleration of the first terminal 302 relative to secondterminal 304 by an amount at least partially or completely eliminatingthe force generated at the first terminal 302 and second terminal 304due to actuation of the movable device 124 by the actuator 202. By usingthe flywheel motor 350 to rotationally accelerate the flywheel 314 atthe start of axial acceleration, the force required to axially move thefirst terminal 302 relative to the second terminal 304 may be reduced oreliminated which may increase the speed at which the actuator 202 movesthe movable device 124 toward a commanded position.

Alternatively, the flywheel motor 350 may be operated in a manner toapply a torque to the flywheel 314 in a direction opposite the rotationof the flywheel 314. In this regard, the application of motor-generatedtorque in a direction opposite the rotation of the flywheel 314 mayresist the torque generated by the relative axial acceleration of thefirst terminal 302 and second terminal 304. In this regard, activecontrol by the flywheel motor 350 may oppose the terminal-developedtorque at the end of actuator 202 motion when the commanded position isreached. In this manner, the step of actively controlling rotation ofthe flywheel 314 may include using the flywheel motor 350 to dynamicallybrake or decelerate the flywheel 314 as the actuator 202 approaches acommanded position to prevent position overshoot.

In a further example, active control of flywheel 314 rotation mayinclude using a brake 360 (e.g., FIGS. 16 and 20) to decelerate theflywheel 314 as the actuator 202 approaches a commanded position of themovable device 124 to prevent position overshoot of the commandedposition. The method may additionally include dynamically braking therotation of the flywheel 314 such as to oppose disturbances (e.g.,undesirable motion) of the actuator 202. The step of dynamically braking(e.g., decelerating or reducing rotational speed) of the flywheel 314may be performed using a brake 360 operatively engageable to theflywheel 314 (e.g., FIGS. 16 and 20) or operatively engageable to abrake rotor (not shown) that may be fixedly coupled to the flywheel 314.Alternatively or additionally, the step of dynamically braking theflywheel 314 may be performed using rotational drag generated by theflywheel motor 350 as described above.

Now referring to FIG. 25, FIG. 25 is a perspective view of an aircraft100 having one or more dual rack and pinion rotational inerter systems500 (see FIGS. 26-30) for damping movement 694 (see FIG. 30) of theflight control surface 122 of the aircraft 100. The aircraft 100 mayinclude the fuselage 102 and the pair of wings 114 extending outwardlyfrom the fuselage 102. The aircraft 100 may include a pair of propulsionunits 115 (e.g., gas turbine engines). As mentioned above, each wing 114may include one or more movable devices 124 configured as flight controlsurfaces 122 of the flight control system 120, where the flight controlsurfaces 122 may be actuated by one or more actuators 202 (see FIG. 26).The flight control surface 122 (see FIGS. 25, 26) may be hingedlycoupled to a support structure 116 (see FIGS. 25, 26) that is rigid,such as the wing 114, including a wing portion support structure 117(see FIG. 26), such as the wing spar 118 (see FIG. 26), or such asanother suitable support structure.

Such flight control surfaces 122 (see FIG. 25) on the wings 114 (seeFIG. 25) may include, but are not limited to, spoilers, ailerons 130(see FIG. 25), and one or more high-lift devices, such as a leading edgeslats and/or trailing edge flaps. At the aft end of the fuselage 102(see FIG. 25), the empennage 104 (see FIG. 25) may include one or morehorizontal tails 110 (see FIG. 25) and the vertical tail 106 (see FIG.25), any one or more of which may include flight control surfaces 122(see FIG. 25) such as the elevator 112 (see FIG. 25), the rudder 108(see FIG. 25), or other types of movable devices 124 (see FIG. 25) thatmay be actuated by one or more actuators 202 (see FIG. 26).

Now referring to FIG. 26, FIG. 26 is a top view of a wing section 114 aof a wing 114, taken along line 26-26 of FIG. 25, illustrating anactuator 202 and a dual rack and pinion rotational inerter system 500operatively coupled between a flight control surface 122, in the form ofan aileron 130, and a support structure 116, such as in the form of awing spar 118 or a wing portion support structure 117. FIG. 26 shows theflight control system 120 comprising the dual rack and pinion rotationalinerter system 500, and the movable device 124, such as the flightcontrol surface 122 in the form of aileron 130. As shown in FIG. 26, theflight control surface 122 may be hingedly coupled to the supportstructure 116 such as in the form of wing 114, including the wingportion support structure 117, the wing spar 118, or such as anothersuitable support structure. The flight control surface 122 (see FIG. 26)may be pivotable or rotatable about a hinge axis 126 (see FIGS. 27-28).The flight control surface 122 preferably comprises the aileron 130, andthe support structure 116 preferably comprises the wing 114, the wingportion support structure 117, the wing spar 118, or another suitablesupport structure.

As shown in FIG. 26, the flight control surface 122, such as the aileron130, comprises a first end 132 and a second end 134. As further shown inFIG. 26, the dual rack and pinion rotational inerter system 500 isattached to the first end 132 of the flight control surface 122, such asthe aileron 130. As further shown in FIG. 26, the dual rack and pinionrotational inerter system 500 may be fixedly attached to the supportstructure 116. The flight control surface 122 (see FIG. 26), such as inthe form of aileron 130 (see FIG. 26), may be actuated by one or moreactuators 202 (see FIG. 26) located on one or both ends of the flightcontrol surface 122 (see FIG. 26), such as the aileron 130 (see FIG.26). In FIG. 26, the actuator 202 and the dual rack and pinionrotational inerter system 500 are provided as separate components andmay each be coupled between the support structure 116, such as the wingportion support structure 117, the wing spar 118, or another suitablesupport structure, and the flight control surface 122, such as theaileron 130. The dual rack and pinion rotational inerter system 500and/or actuator 202 may be positioned anywhere along the wing spar 118and the aileron 130 for desired and advantageous structural strength,rigidity, aircraft weight, and/or installation cost. In particular, thedual rack and pinion rotational inerter system 500 may be applied to anyflight control surface that comprises a flutter critical surface.

Now referring to FIG. 27, FIG. 27 is a sectional view of the wingsection 114 a of the wing 114, taken along line 27-27 of FIG. 26, andillustrating an example of a dual rack and pinion rotational inertersystem 500 installed between the movable device 124, such as the flightcontrol surface 122, for example, the aileron 130, and the supportstructure 116, such as the wing spar 118. FIG. 27 shows a hinge axis 126of the movable device 124, such as the flight control surface 122, forexample, the aileron 130. The movable device 124, such as the flightcontrol surface 122, for example, the aileron 130 is attached or coupledto a pivot element 127, such as in the form of a bellcrank 128.Alternatively, the pivot element 127 may comprise a horn element 136(see FIG. 30) and a bearing element 138 (see FIG. 30), or anothersuitable pivot element 127. The pivot element 127 connects the movabledevice 124, such as the flight control surface 122, for example, theaileron 130 to a first terminal 502, such as a spherical bearing 574, ofthe dual rack and pinion rotational inerter system 500.

As shown in FIG. 27, the dual rack and pinion rotational inerter system500 comprises a flexible holding structure 506 disposed between themovable device 124, such as the flight control surface 122, for example,the aileron 130, and the support structure 116 of the aircraft 100 (seeFIG. 25). The flexible holding structure 506 (see FIG. 27) may comprisea clamping holding structure 506 a (see FIG. 27), may comprise a thinsection flexure holding structure 506 b (see FIG. 29A), or may compriseanother suitable flexible holding structure 506 (see FIG. 27).

As shown in FIG. 27, the dual rack and pinion rotational inerter system500 further comprises a dual rack and pinion assembly 550 held orclamped by and between the flexible holding structure 506. The dual rackand pinion assembly 550 (see FIG. 27) comprises dual racks 552 (see FIG.27) positioned opposite each other and substantially housed within andheld or clamped by the flexible holding structure 506 (see FIG. 27). Theracks 552 (see FIG. 27) comprise a first rack 552 a (see FIG. 27) and asecond rack 552 b (see FIG. 27), each of the first rack 552 a and thesecond rack 552 b having a plurality of teeth 570 (see FIG. 27).

As shown in FIG. 27, the dual rack and pinion assembly 550 furthercomprises a pinion 596, such as in the form of a pinion gear 596 a,engaged to and between the first rack 552 a and the second rack 552 b.As further shown in FIG. 27, the pinion 596, such as in the form of thepinion gear 596 a, has a plurality of gear teeth 602 configured toengage the teeth 570 of the first rack 552 a and the second rack 552 b,and has a through opening 604. The through opening 604 (see FIGS. 27,29A) may have a circle shaped cross section 606 a (see FIG. 27), mayhave a square shaped cross section 606 b (see FIG. 29A), or may haveanother suitable geometric shaped cross-section.

As used herein, “dual rack and pinion” means a type of linear actuatorusing a circular gear called a pinion to engage two linear gear barscalled racks, where rotational motion applied to the pinion causes theracks to move relative to each other and relative to the pinion, thustranslating the rotational motion of the pinion into linear motion.

As shown in FIG. 27, the dual rack and pinion rotational inerter system500 further comprises the first terminal 502 coupled to the first rack552 a and coupled to the flight control surface 122, via the pivotelement 127, and a second terminal 503 coupled to the second rack 552 b,and coupled to the support structure 116. The first terminal 502 (seeFIG. 27) preferably comprises a spherical bearing 574, such as in theform of a first spherical bearing 574 a, and the second terminal 503preferably comprises a spherical bearing 574, such as in the form of asecond spherical bearing 574 b. Each of the spherical bearings 574comprises a rack attachment portion 580 and a spherical ball bearingportion 582 having a ball bearing 590. As shown in FIG. 27, the firstrack 552 a is attached to the first terminal 502, such as in the form offirst spherical bearing 574 a, and the second rack 552 b is attached tothe second terminal 503, such as in the form of a second sphericalbearing 574 b.

As shown in FIG. 27, the dual rack and pinion rotational inerter system500 further comprises a pair of inertia wheels 660 comprising a firstinertia wheel 660 a aligned opposite to a second inertial wheel 660 b.The inertia wheels 660 (see FIG. 27) are each respectively positionedadjacent to opposite exterior sides (e.g., a first side 539 a (see FIG.29C) and a second side 539 b (see FIG. 29C)) of the flexible holdingstructure 506. As shown in FIG. 27, the dual rack and pinion rotationalinerter system 500 further comprises an axle element 612 insertedcontinuously through the first inertial wheel 660 a, through theflexible holding structure 506, through the pinion 596, and through thesecond inertial wheel 660 b.

Rotation of the flight control surface 122 (see FIG. 27) causestranslational movement 610 (see FIG. 30), via the pivot element 127 (seeFIG. 27), of the first rack 552 a (see FIG. 27) relative to the secondrack 552 b (see FIG. 27), along the longitudinal inerter axis 504 (seeFIG. 27), which causes the rotational movement 611 (see FIG. 30) of thepinion 596 (see FIG. 27) and the pair of inertia wheels 660 (see FIG.27), such that the rotational movement 611 of the pinion 596 is resistedby the pair of inertia wheels 660 and there is no incidental motion 698(see FIG. 30). This results in the dual rack and pinion rotationalinerter system 500 (see FIG. 27) damping movement 694 (see FIG. 30) ofthe flight control surface 122.

The motion of the pinion 596 (see FIG. 27) is resisted by the inertialwheels 660 (see FIG. 27), such that the change of orientation of theracks 552 (see FIG. 27) are only in relation to the longitudinal inerteraxis 504 (see FIG. 27) by inducing a resistance force 704 (see FIG. 30)to the rotation of the first terminal 502 (see FIG. 27) connected to theflight control surface 122 (see FIGS. 27, 30) of the aircraft 100 (seeFIGS. 25, 30). The resistance force 704 (see FIG. 30) is resisted by theinertial wheels 660 (see FIGS. 27, 30) with the through hole 666 (seeFIG. 29A) having the square shaped cross-section 668 a (see FIG. 30) andwith the axle element 612 (see FIG. 27) having the central rectangularportion 618 (see FIG. 29A) having the square shaped cross-section 626(see FIG. 29A). Damping movement 694 (see FIG. 30) of the flight controlsurface 122 (see FIG. 27) preferably provides increased fluttersuppression 708 (see FIG. 30) of the flight control surface 122. Thispreferably results in an improved hydraulic application stability 710(see FIG. 30) and an increased efficient flight control actuation 712(see FIG. 30). The dual rack and pinion rotational inerter system 500(see FIGS. 27, 30) of the aircraft 100 (see FIG. 30) provides a passivesolution 714 (see FIG. 30), that is, the dual rack and pinion rotationalinerter system 500 uses a passive means to change the dynamics of theflight control system 120 (see FIG. 30) instead of active controlelements, such as one or more actuators 202 (see FIG. 30) and valve sizeor diameter of hydraulic actuators 204 (see FIG. 28).

Now referring to FIG. 28, FIG. 28 is a sectional view of the wingsection 114 a of a wing 114, taken along line 28-28 of FIG. 26, andillustrating an example of the actuator 202, such as in the form of ahydraulic actuator 204, mechanically coupled between the supportstructure 116, such as the wing spar 118, and the movable device 124,such as the flight control surface 122, for example, the aileron 130.FIG. 28 shows the hinge axis 126 of the movable device 124, such as theflight control surface 122, for example, the aileron 130. The movabledevice 124, such as the flight control surface 122, for example, theaileron 130 is attached or coupled to the pivot element 127, such as inthe form of bellcrank 128. Alternatively, the pivot element 127 maycomprise the horn element 136 (see FIG. 30) and the bearing element 138(see FIG. 30), or another suitable pivot element 127. The pivot element127 connects the movable device 124, such as the flight control surface122, for example, the aileron 130 to a rod end 214 of the actuator 202,such as the hydraulic actuator 204.

FIG. 28 further shows an example of the actuator 202, such as in theform of a hydraulic actuator 204 that is linear, and that ismechanically coupled between the support structure 116, such as the wingspar 118, and one end of the movable device 124, such as the flightcontrol surface 122, for example, the aileron 130. As shown in FIG. 28,the actuator 202, such as in the form of hydraulic actuator 204,includes a piston 216 coupled to a piston rod 224. The piston 216 (seeFIG. 28) is slidable within an actuator housing 228 (see FIG. 7) (e.g.,a cylinder). The actuator 202 (see FIG. 28), such as in the form ofhydraulic actuator 204 (see FIG. 28), further includes the rod end 214(see FIG. 28) and a cap end 212 (see FIG. 28) axially movable relativeto one another in response to pressurized hydraulic fluid acting in anunbalanced manner on one or both sides of the piston 216 (see FIG. 28)inside the actuator housing 228 (see FIG. 7). In the example shown inFIG. 28, the rod end 214 of the actuator 202, such as the hydraulicactuator 204, is coupled to the bellcrank 128. The bellcrank 128 (seeFIG. 28) is hingedly coupled to the flight control surface 122 (see FIG.28), such as the aileron 130 (see FIG. 28), in a manner such that linearactuation of the hydraulic actuator 204 (see FIG. 28) causes pivoting ofthe flight control surface 122, such as the aileron 130, about the hingeaxis 126 (see FIG. 28). Alternatively, instead of the bellcrank 128, thehorn element 136 (see FIG. 30) and bearing element 138 (see FIG. 30) maybe used as a connection between the rod end 214 of the actuator 202 andthe flight control surface 122. The cap end 212 (see FIG. 28) of theactuator 202 (see FIG. 28), such as the hydraulic actuator 204 (see FIG.28), is coupled to the wing spar 118 (see FIG. 28).

Now referring to FIG. 29A, FIG. 29A is an exploded perspective view ofan example of a dual rack and pinion rotational inerter system 500 ofthe disclosure, in a disassembled position 505 a. As shown in FIG. 29A,the dual rack and pinion rotational inerter system 500 comprises aflexible holding structure 506 configured to be disposed between themovable device 124 (see FIG. 27), such as the flight control surface 122(see FIG. 27), for example, the aileron 130 (see FIG. 27), and thesupport structure 116 (see FIG. 27) of the aircraft 100 (see FIG. 25).The flexible holding structure 506 (see FIG. 29A) may be in the form ofa clamping holding structure 506 a (see FIG. 27), a thin section flexureholding structure 506 b (see FIG. 29A), or may comprise another suitableflexible holding structure 506 (see FIG. 27). The flexible holdingstructure 506 (see FIGS. 29A, 30) may comprise a two-piece flexibleholding structure 506 c (see FIG. 30) comprised of two pieces 508 (seeFIG. 29A), including a first piece 508 a (see FIG. 29A) configured forattachment to, and attached to upon assembly, a second piece 508 b (seeFIG. 29A). Preferably, the first piece 508 a (see FIG. 29A) is a mirrorimage 509 (see FIG. 30) of the second piece 508 b (see FIG. 29A). In oneversion, the two-piece flexible holding structure 506 c (see FIG. 30)may be comprised of mirror image plates 510 (see FIG. 30). Each mirrorimage plate 510 (see FIG. 30) may comprise a forged plate 510 a (seeFIG. 30), an extruded plate 510 b (see FIG. 30), or another suitabletype of plate.

As shown in FIG. 29A, each of the two pieces 508, such as the firstpiece 508 a and the second piece 508 b, comprises a first end 512 a, asecond end 512 b, and a body 514 formed therebetween. The first end 512a (see FIG. 29A) and the second end 512 b (see FIG. 29A) have cut-outportions 532 shaped to accommodate racks 552 (see FIG. 29A) of the dualrack and pinion assembly 550 (see FIG. 29A). As further shown in FIG.29A, As shown in FIG. 29A, each of the two pieces 508, such as the firstpiece 508 a and the second piece 508 b, comprises an exterior 516 a, aninterior 516 b, a top side 528, and a bottom side 530. The interior 516b (see FIG. 29A) includes interior corners 534 (see FIG. 29A) andinterior longitudinal edges 536 (see FIG. 29A) configured to receive andretain each of a plurality of rod bearings 540 (see FIG. 29A).

As shown in FIG. 29A, each of the two pieces 508, such as the firstpiece 508 a and the second piece 508 b, comprises a primary throughopening 518 (see FIGS. 29A, 30) positioned centrally through the body514 of each piece 508, and configured to receive, and receiving, theaxle element 612. As shown in FIG. 29A, each of the two pieces 508, suchas the first piece 508 a and the second piece 508 b, further comprises afirst secondary through opening 520 a configured to receive, andreceiving, a fastener 522, such as in the form of a bolt 522 a, oranother suitable fastener, and a second secondary through opening 520 bconfigured to receive, and receiving, another fastener 522, such as inthe form of a bolt 522 a, or another suitable fastener. Each of thefasteners 522 (see FIG. 29A), such as the bolts 522 a (see FIG. 29A),may be inserted through and coupled to a washer 524 (see FIG. 29A), suchas a first washer 524 a (see FIG. 29A), which is preferably positionedagainst the exterior 516 a (see FIG. 29A) of the second piece 508 b (seeFIG. 29A). Each of the fasteners 522 (see FIG. 29A), such as the bolts522 a (see FIG. 29A), may be further inserted through and coupled to awasher 524 (see FIG. 29A), such as a second washer 524 b (see FIG. 29A),which is preferably positioned against the exterior 516 a (see FIG. 29A)of the first piece 508 a (see FIG. 29A), and further inserted throughand coupled to a nut 526 (see FIG. 29A).

The flexible holding structure 506 (see FIGS. 29A-29C) further has anend through opening 538 (see FIGS. 29A-29C) formed through the firstends 512 a (see FIGS. 29A-29B) and the second ends 512 b (see FIGS.29A-29B), when the two pieces 508 (see FIGS. 29A-29B) of the flexibleholding structure 506 are joined together in an assembled position 505 b(see FIG. 29B).

As shown in FIG. 29A, the dual rack and pinion rotational inerter system500 further comprises a plurality of rod bearings 540 inserted into theinterior corners 534 and along the interior longitudinal edges 536 ofthe flexible holding structure 506. As shown in FIG. 29A, a rod bearing540, such as a first rod bearing 540 a, may be installed at and along anupper interior longitudinal edge 536 a of the first piece 508 a of theflexible holding structure 506, and a rod bearing 540, such as a secondrod bearing 540 b, may be installed at and along a lower interiorlongitudinal edge 536 b of the first piece 508 a of the flexible holdingstructure 506.

As further shown in FIG. 29A, a rod bearing 540, such as a third rodbearing 540 c, may be installed at and along an upper interiorlongitudinal edge 536 a of the second piece 508 b of the flexibleholding structure 506, and a rod bearing 540, such as a fourth rodbearing 540 d, may be installed at and along a lower interiorlongitudinal edge 536 b of the second piece 508 b of the flexibleholding structure 506.

Each rod bearing 540 (see FIG. 29A) comprises a first end 542 a (seeFIG. 29A), a second end 542 b (see FIG. 29A), a longitudinal body 544(see FIG. 29A) formed between the first end 542 a and the second end 542b, exterior sides 546 a (see FIG. 29A), and interior sides 546 b (seeFIG. 29A). Each rod bearing 540 (see FIG. 29A) further comprises alinear slide track 548 (see FIG. 29A) formed along an interior side 546b (see FIG. 29A) to facilitate translation of the racks 552 (see FIG.29A) along the rod bearings 540 (see FIG. 29A) and through the flexibleholding structure 506 (see FIG. 29A).

As shown in FIG. 29A, the dual rack and pinion rotational inerter system500 further comprises a dual rack and pinion assembly 550 held orclamped by and between the flexible holding structure 506. As furthershown in FIG. 29A, the dual rack and pinion assembly 550 comprises racks552, such as the first rack 552 a and the second rack 552 b, andcomprises the pinion 596, such as the pinion gear 596 a, engaged to andbetween the first rack 552 a and the second rack 552 b.

As shown in FIG. 29A, each of the racks 552, such as the first rack 552a and the second rack 552 b, comprises a first end 554 a, a second end554 b, and a longitudinal body 556 formed between the first end 554 aand the second end 554 b. As further shown in FIG. 29A, the longitudinalbody 556 of each of the racks 552, such as the first rack 552 a and thesecond rack 552 b, comprises a spherical bearing attachment portion 558and a linear gear portion 560, and an interior side 572 a and anexterior side 572 b.

The spherical bearing attachment portion 558 comprises one or morefastener holes 562 configured to receive, and receiving, one or morefasteners 564, such as in the form of bolts 564 a, or another suitablefastener. Each of the fasteners 564 (see FIG. 29A), such as the bolts564 a (see FIG. 29A), may be inserted through and coupled to a washer566 (see FIG. 29A), such as a first washer 566 a (see FIG. 29A), whichis preferably positioned against the exterior side 572 b (see FIG. 29A)of the racks 552 (see FIG. 29A). Each of the fasteners 564 (see FIG.29A), such as the bolts 564 a (see FIG. 29A), may be further insertedthrough and coupled to a washer 566 (see FIG. 29A), such as a secondwasher 566 b (see FIG. 29A), which is preferably positioned against anexterior side 579 a (see FIG. 29A) of a spherical bearing 574 (see FIG.29A), and further inserted through and coupled to a nut 568 (see FIG.29A).

The linear gear portion 560 (see FIG. 29A) of each rack 552 comprises aplurality of teeth 570 projecting from the interior side 572 a of therack 552. As shown in FIG. 29A, the first rack 552 a has a firstplurality of teeth 570 a, and the second rack 552 b has a secondplurality of teeth 570 b. The first rack 552 a (see FIGS. 29A-29B) ispreferably positioned opposite to the second rack 552 b (see FIGS.29A-29B), with the first plurality of teeth 570 a (see FIGS. 29A-29B) onthe first rack 552 a facing opposite the second plurality of teeth 570 b(see FIGS. 29A-29B) on the second rack 552 b.

As shown in FIG. 29A, the dual rack and pinion assembly 550 furthercomprises the pinion 596, such as in the form of the pinion gear 596 a,or another suitable pinion. As shown in FIG. 29A, the pinion 596, suchas the pinion gear 596 a, comprises a first face 598 a, a second face598 b, an exterior 600 a, an interior 600 b, a body 601, and a pluralityof gear teeth 602 formed on and projecting from the exterior 600 a ofthe pinion 596. As further shown in FIG. 29A, the pinion 596, such asthe pinion gear 596 a, has a through opening 604 having a square shapedcross-section 606 b. Alternatively, the through opening 604 may have acircle shaped cross-section 606 a (see FIGS. 27, 30), or anothergeometric shaped cross-section. The pinion 596 (see FIG. 29A), such asthe pinion gear 596 a (see FIG. 29A), is configured to be engaged to,and is engaged to, and positioned between, the first rack 552 a (seeFIG. 29A) and the second rack 552 b (see FIG. 29A). As shown in FIG.29B, preferably, the gear teeth 602 of the pinion 596 engage with thefirst plurality of teeth 570 a on the first rack 552 a and engage withthe second plurality of teeth 570 b on the second rack 552 b. As shownin FIG. 30, the pinion 596 has a thickness 608 and a diameter 610.

As shown in FIG. 29A, the dual rack and pinion rotational inerter system500 further comprises the first terminal 502 configured to be coupled tothe first rack 552 a, and comprises the second terminal 503 configuredto be coupled to the second rack 552 b. The first terminal 502 and thesecond terminal 503 preferably comprise spherical bearings 574, such asin the form of spherical ball bearing rods 575 (see FIG. 30). The firstterminal 502 (see FIG. 29A) preferably comprises a spherical bearing 574(see FIG. 29A), such as in the form of a first spherical bearing 574 a(see FIG. 29A), and the second terminal 503 (see FIG. 29A) preferablycomprises a spherical bearing 574, such as in the form of a secondspherical bearing 574 b (see FIG. 29A). As shown in FIG. 29A, the firstspherical bearing 574 a has a first end 576 a, a second end 576 b, and abody 578 formed between the first end 576 a and the second end 576 b. Asfurther shown in FIG. 29A, the second spherical bearing 574 b has afirst end 577 a, a second end 577 b, and a body 578 formed between thefirst end 577 a and the second end 577 b. Each of the spherical bearings574 (see FIG. 29A) has an exterior side 579 a (see FIG. 29A), aninterior side 579 b (see FIG. 29A), a rack attachment portion 580 (seeFIG. 29A), and a spherical ball bearing portion 582 (see FIG. 29A).

The rack attachment portion 580 (see FIG. 29A) of each spherical bearing574 (see FIG. 29A) has one or more fastener holes 584 (see FIG. 29A)configured to receive, and receiving, the one or more fasteners 564 (seeFIG. 29A), such as in the form of bolts 564 a (see FIG. 29A), or anothersuitable fastener. Each of the fasteners 564 (see FIG. 29A), such as thebolts 564 a (see FIG. 29A), may be inserted through the sphericalbearing attachment portions 558 (see FIG. 29A) of the racks 552 (seeFIG. 29A) and through the rack attachment portions 580 (see FIG. 29A) ofthe spherical bearings 574 (see FIG. 29A) to attach the respectivespherical bearings 574 (see FIG. 29A) to the respective racks 552 (seeFIG. 29A). As shown in FIG. 29A, each rack attachment portion 580 hasthickness 586.

As further shown in FIG. 29A, each spherical ball bearing portion 582has an interior opening 588 that preferably houses or retains one ormore ball bearings 590. The spherical ball bearing portion 582 (see FIG.29A) preferably has a spherical shape 592 (see FIG. 29A) and a diameter594 (see FIG. 29A). Preferably, the diameter 594 of the spherical ballbearing portion 582 is greater than the thickness 586 of the rackattachment portion 580 for each spherical bearing 574.

As shown in FIG. 29A, the dual rack and pinion rotational inerter system500 further comprises a pair of inertia wheels 660 comprising a firstinertia wheel 660 a and a second inertial wheel 660 b. As further shownin FIG. 29A, each of the pair of inertia wheels 660 has a first interiorface 662 a, a second exterior face 662 b, a body 664, and a throughopening 666. The through opening 666 (see FIG. 29A) may have a squareshaped cross-section 668 a (see FIGS. 29A, 30), a circle shapedcross-section 668 b (see FIG. 30), or another suitable geometric shapedcross-section. The through opening 666 (see FIG. 29A) of each inertiawheel 660 (see FIG. 29A) may have a smooth interior, or may have aspline interior 670 (see FIG. 30) that corresponds to a mating splineportion that may be formed on the axle element 612 (see FIG. 29A). Asused herein, “spline” means ridges or teeth on a surface that mesh withgrooves in a mating or corresponding piece and transfer torque to it,maintaining the angular correspondence between them. Each inertia wheels660 (see FIG. 29A) has a thickness 672 (see FIG. 29A).

As shown in FIG. 29A, the dual rack and pinion rotational inerter system500 further comprises the axle element 612. The axle element 612 (seeFIG. 29A) is configured to be inserted through, and is inserted through,the first inertial wheel 660 a (see FIG. 29A), the flexible holdingstructure 506 (see FIG. 29A), the pinion 596 (see FIG. 29A), and thesecond inertial wheel 660 b (see FIG. 29A). The axle element 612 (seeFIG. 29A) couples a rotational movement 611 (see FIG. 30) of the pair ofinertia wheels 660 (see FIG. 29A) and the pinion 596 (see FIG. 29A).

As shown in FIG. 29A, the axle element 612 has a first end 614 a, asecond end 614 b, and a body 616 formed between the first end 614 a andthe second end 614 b. As further shown in FIG. 29A, the body 616 of theaxle element 612 comprises a central rectangular portion 618, acylindrical portion 632 attached to each end 624 of the centralrectangular portion 618, a square portion 634 attached to each end 633(see FIG. 29C) of each cylindrical portion 632, and a cylindricalthreaded end portion 640 attached to each end 638 (see FIG. 29C) of eachsquare portion 634. As shown in FIG. 29A, the central rectangularportion 618 has sides 620, for example, four sides 620, each with a sidesurface 628 and a length 622. The central rectangular portion 618 (seeFIG. 29A) further has ends 624 (see FIG. 29A), for example, two ends624. The central rectangular portion 618 (see FIG. 29A) preferably has asquare shaped cross-section 626 (see FIGS. 29A, 30).

One or more shims 630 (see FIG. 29A), such as shim stock, may be appliedto one or more side surfaces 628 (see FIG. 29A) of the centralrectangular portion 618 (see FIG. 29A) prior to applying a sleeveelement 646 (see FIG. 29A), discussed below. FIG. 29A shows shims 630comprising a first shim 630 a and a second shim 630 b configured to beapplied to side surfaces 628.

Preferably, the cylindrical portions 632 (see FIG. 29A) of the axleelement 612 each have a circle shaped cross-section 631 (see FIG. 30).Preferably, the square portions 634 (see FIG. 29A) of the axle element612 each have a square shaped cross-section 638 (see FIG. 30).Preferably, the cylindrical threaded end portions 640 (see FIG. 29A) ofthe axle element 612 each have a circle shaped cross-section 644 (seeFIG. 30). As shown in FIG. 29A, the cylindrical threaded end portions640 have exterior threads 642 for threaded engagement with axlecylindrical threaded end portion nuts 688, such as first axlecylindrical threaded end portion nut 688 a and second axle cylindricalthreaded end portion nut 688 b.

The axle element 612 (see FIGS. 29A, 30) controls a clamping force 700(see FIG. 30) of the flexible holding structure 506 (see FIGS. 29A, 30),and controls a slide friction 702 of the inertia wheels 660 (see FIGS.29A, 30). To prevent or minimize deflection of the flexible holdingstructure 506, the clamping force 700 (see FIG. 30) may be applied boththrough the axle element 612 (see FIGS. 29A, 30) and through the one ormore fasteners 522 (see FIG. 29A), such as bolts 522 a (see FIG. 29A)inserted through the flexible holding structure 506 (see FIG. 29A).

As shown in FIG. 29A, the dual rack and pinion rotational inerter system500 may further comprise a sleeve element 646 configured to be slippedor applied over the central rectangular portion 618 of the axle element612. As shown in FIG. 29A, the sleeve element 646 comprises a first end648 a, a second end 648 b, and a body 650 formed between the first end648 a and the second end 648 b. As shown in FIG. 29A, the sleeve element646 further comprises sides 652, for example, four sides 652, eachhaving a length 658, and further comprises ends 654, for example, twoends 654. As further shown in FIG. 29A, the sleeve element 646 has athrough opening 656, such as in the form of a square shaped throughopening 656 a. If the sleeve element 646 is used, the sleeve element 646is preferably applied or slipped over the central rectangular portion618 and over the shims 630, if the shims 630 are used, prior to the axleelement 612 being inserted through the pinion 596. Preferably, thethickness 608 (see FIG. 30) of the pinion (see FIG. 30) is equal to, orsubstantially equal to, the length 658 (see FIG. 29A) of the sleeveelement 646 (see FIG. 29A). If no sleeve element 646 is present,preferably the thickness 608 (see FIG. 30) of the pinion (see FIG. 30)is equal to, or substantially equal to, the length 622 (see FIG. 29A) ofthe central rectangular portion 618 (see FIG. 29A).

As shown in FIG. 29A, the dual rack and pinion rotational inerter system500 may further comprise one or more axle square portion washers 674,such as a first axle square portion washer 674 a and a second axlesquare portion washer 674 b for engagement with and coupling to eachsquare portion 634 of the axle element 612. As shown in FIG. 29A, eachaxle square portion washer 674 comprises an interior face 676 a, anexterior face 676 b, a body 678 formed between the interior face 676 aand the exterior face 676 b, and a through opening 680 formed throughthe body 678, and preferably through the center of the body 678. Thethrough opening 680 (see FIG. 29A) may have a square shapedcross-section 682 a (see FIG. 29A, 30), a circle shaped cross-section682 b (see FIG. 30), or another suitable geometric shaped cross-section.Each axle square portion washer 674 (see FIG. 29A) has a thickness 684(see FIG. 29A).

As shown in FIG. 29A, the dual rack and pinion rotational inerter system500 may further comprise one or more axle cylindrical threaded endportion washers 686, such as a first axle cylindrical threaded endportion washer 686 a and a second first axle cylindrical threaded endportion washer 686 b, configured for engagement with and coupling toeach cylindrical threaded end portion 640 of the axle element 612.

As shown in FIG. 29A, the dual rack and pinion rotational inerter system500 may further comprise one or more axle cylindrical threaded endportion nuts 688, such as a first axle cylindrical threaded end portionnut 688 a and a second axle cylindrical threaded end portion nut 688 b,configured for engagement with and coupling to each cylindrical threadedend portion 640 of the axle element 612.

Now referring to FIG. 29B, FIG. 29B is a perspective view of the dualrack and pinion rotational inerter system 500 of FIG. 29A in anassembled position 505 b. As shown in FIG. 29B, the dual rack and pinionrotational inerter system 500 comprises the flexible holding structure506, such as in the form of thin section flexure holding structure 506b. The flexible holding structure 506 (see FIG. 29B) comprises twopieces 508 (see FIG. 29B), including the first piece 508 a (see FIG.29B) attached to the second piece 508 b (see FIG. 29B). FIG. 29B showsan attachment seam 690 where the two pieces 508 are joined together.Preferably, the first piece 508 a (see FIG. 29B) is a mirror image 509(see FIG. 30) of the second piece 508 b (see FIG. 29B). FIG. 29B showsthe first end 512 a, the second end 512 b, the first side 539 a, thesecond side 539 b, and the end through opening 538 of the flexibleholding structure 506.

FIG. 29B shows the first secondary through opening 520 a and the secondsecondary through opening 520 b with the fastener 522 inserted througheach of the first secondary through opening 520 a and the secondsecondary through opening 520 b. FIG. 29B further shows the plurality ofrod bearings 540 installed in the interior of the flexible holdingstructure 506. For example, FIG. 29B shows the first rod bearing 540 a,the third rod bearing 540 c, and the fourth rod bearing 540 d.

FIG. 29B shows the dual rack and pinion assembly 550 held or clamped byand between the flexible holding structure 506. As shown in FIG. 29B,the dual rack and pinion assembly 550 comprises the racks 552, such asthe first rack 552 a and the second rack 552 b, and comprises the pinion596, such as the pinion gear 596 a, engaged to and between the firstrack 552 a and the second rack 552 b. FIG. 29B shows the first pluralityof teeth 570 a of the first rack 552 a facing opposite the secondplurality of teeth 570 b of the second rack 552 b. FIG. 29B furthershows the gear teeth 602 of the pinion 596 engaged with the firstplurality of teeth 570 a on the first rack 552 a and engaged with thesecond plurality of teeth 570 b on the second rack 552 b.

As shown in FIG. 29B, the dual rack and pinion rotational inerter system500 further comprises the first terminal 502 coupled to the first rack552 a, and comprises the second terminal 503 coupled to the second rack552 b. The first terminal 502 (see FIG. 29B) and the second terminal 503(see FIG. 29B) comprise spherical bearings 574 (see FIG. 29B), such asin the form of the first spherical bearing 574 a (see FIG. 29B) and thesecond spherical bearing 574 b (see FIG. 29B). Each of the sphericalbearings 574 (see FIG. 29B) has the rack attachment portion 580 (seeFIG. 29B) and the spherical ball bearing portion 582 (see FIG. 29B). Therack attachment portion 580 (see FIG. 29B) of each spherical bearing 574(see FIG. 29B) has one or more fastener holes 584 (see FIG. 29B). FIG.29B shows the fastener 564 inserted through the fastener hole 584 andinserted through the washer 566 and the nut 568. The spherical ballbearing portion 582 (see FIG. 29B) of each spherical bearing 574 (seeFIG. 29B) has an interior opening 588 with one or more ball bearings 590(see FIG. 29B).

As shown in FIG. 29B, the dual rack and pinion rotational inerter system500 further comprises the pair of inertia wheels 660 comprising thefirst inertia wheel 660 a aligned opposite the second inertial wheel 660b. FIG. 29B shows the through opening 666 of the inertia wheel 660 bwith the axle element 612 inserted through the through opening 666. FIG.29B further shows the axle element 612 inserted through the axlecylindrical threaded end portion washer 686 and the axle cylindricalthreaded end portion nut 688. The axle element 612 (see FIG. 29B) isalso inserted through the first inertial wheel 660 a (see FIG. 29B), theflexible holding structure 506 (see FIG. 29B), the pinion 596 (see FIG.29B), and the second inertial wheel 660 b (see FIG. 29B). The axleelement 612 (see FIG. 29B) couples the rotational movement 611 (see FIG.30) of the pair of inertia wheels 660 (see FIG. 29B) and the pinion 596(see FIG. 29B).

Now referring to FIG. 29C, FIG. 29C is a cross-sectional view of thedual rack and pinion rotational inerter system 500 in the assembledposition 505 b, of FIG. 29B, taken along lines 29C-29C of FIG. 29B. FIG.29C shows the dual rack and pinion rotational inerter system 500 withthe flexible holding structure 506, such as in the form of thin sectionflexure holding structure 506 b. FIG. 29C shows the two pieces of theflexible holding structure 506, including the first piece 508 a attachedor joined to the second piece 508 b. FIG. 29C shows the attachment seam690 where the two pieces 508 are joined together and shows the firstside 539 a and the second side 539 b of the flexible holding structure506. FIG. 29C further shows the primary through opening 518 through thefirst piece 508 a and the second piece 508 b and through which the axleelement 612 is inserted through. FIG. 29C further shows the plurality ofrod bearings 540, including the first rod bearing 540 a, the second rodbearing 540 b, the third rod bearing 540 c, and the fourth rod bearing540 d installed within and at the corners of the flexible holdingstructure 506.

FIG. 29C shows the racks 552 of the dual rack and pinion assembly 550(see FIG. 29B), including the first rack 552 a and the second rack 552b. FIG. 29C further shows the pinion 596, such as the pinion gear 596 a,of the dual rack and pinion assembly 550 (see FIG. 29B). The pinion 596,such as the pinion gear 596 a has the plurality of gear teeth 602 (seeFIG. 29C) engaged with and coupled between the plurality of teeth 570(see FIG. 29C) of the first rack 552 a and the second rack 552 b. FIG.29C further shows the gear teeth 602 of the pinion 596 engaged with thefirst plurality of teeth 570 a on the first rack 552 a and engaged withthe second plurality of teeth 570 b on the second rack 552 b. FIG. 29Cfurther shows the through opening 604 of the pinion 596 through whichthe axle element 612 is inserted through and through which the centralrectangular portion 618 of the axle element 612 aligns with the throughopening 604 of the pinion 596. FIG. 29C shows the shim 630 positionedbetween the central rectangular portion 618 of the axle element 612 andthe sleeve element 646. FIG. 29C further shows the sleeve element 646between the shim 630 and the pinion 596.

FIG. 29C further shows the pair of inertia wheels 660 comprising thefirst inertia wheel 660 a aligned opposite the second inertial wheel 660b. The inertia wheels 660 (see FIG. 27) are each respectively positionedadjacent to opposite exterior sides, such as the first side 539 a andthe second side 539 b of the flexible holding structure 506. FIG. 29Cfurther shows the through opening 666 of the inertia wheels 660 with theaxle element 612 inserted through the through opening 666. FIG. 29Cfurther shows the axle element 612 inserted through the axle cylindricalthreaded end portion nut 688, including the first axle cylindricalthreaded end portion nut 688 a and the second axle cylindrical threadedend portion nut 688 b. FIG. 29C further shows the axle element 612inserted through the axle cylindrical threaded end portion washer 686,including the first axle cylindrical threaded end portion washer 686 aand the second axle cylindrical threaded end portion washer 686 b. FIG.29C further shows the axle element 612 inserted through the throughopening 680 of the axle square portion washer 674, including the firstaxle square portion washer 674 a and the second axle square portionwasher 674 b.

FIG. 29C shows the axle element 612 having the first end 614 a and thesecond end 614 b and comprising the central rectangular portion 618, thecylindrical portion 632 attached to each end 624 (see FIG. 29A) of thecentral rectangular portion 618, the square portion 634 attached to eachend 633 of each cylindrical portion 632, and the cylindrical threadedend portion 640 attached to each end 638 of each square portion 634. Asshown in FIG. 29C, the axle element 612 is also inserted continuouslythrough the first inertial wheel 660 a, through the flexible holdingstructure 506, through the pinion 596, and through the second inertialwheel 660 b. The axle element 612 (see FIG. 29C) controls a clampingforce 700 (see FIG. 30) of the flexible holding structure 506 (see FIG.29C), and controls a slide friction 702 of the inertia wheels 660 (seeFIG. 29C). the flexible holding structure 506 (see FIG. 29A). The axleelement 612 (see FIG. 29C) further couples the rotational movement 611(see FIG. 30) of the pair of inertia wheels 660 (see FIG. 29C) and thepinion 596 (see FIG. 29C).

Now referring to FIG. 30, FIG. 30 is a block diagram of a flight controlsystem 120 of an aircraft 100, including one or more actuators 202configured to actuate, or actuating, a movable device 124, such as aflight control surface 122, for example, an aileron 130, about a hingeaxis 126, and further including at least one dual rack and pinionrotational inerter system 500 for damping movement 694 of the movabledevice 124, such as the flight control surface 122, for example, theaileron 130.

The aircraft 100 (see FIG. 30) comprises the flight control surface 122(see FIG. 30) pivotably coupled to a support structure 116 (see FIG.30). As shown in FIG. 30, the support structure 116 may comprise a wing114, a wing portion support structure 117, a wing spar 118, or anothersuitable support structure 116. As further shown in FIG. 30, theactuator 202 comprises the cap end 212, the piston 216, the piston rod,224, and the rod end 214. As shown in FIG. 30, the movable device 124,such as the flight control surface 122, for example, the aileron 130,may be coupled to a pivot element 127. The pivot element 127 (see FIG.30) may comprise a bellcrank 128 (see FIG. 30), may comprise a hornelement 136 (see FIG. 30) and a bearing element 138 (see FIG. 30), ormay comprise another suitable pivot element 127.

As shown in FIG. 30, the aircraft 100 further comprises at least onedual rack and pinion rotational inerter system 500 for damping movement694 of the flight control surface 122. The dual rack and pinionrotational inerter system 500 (see FIG. 30), as discussed in detailabove, comprises a flexible holding structure 506 (see FIG. 30) disposedbetween the flight control surface 122 (see FIG. 30) and the supportstructure 116 (see FIG. 30) of the aircraft 100 (see FIG. 30). As shownin FIG. 30, the flexible holding structure 506 may be in the form of aclamping holding structure 506 a (see also FIG. 27), a thin sectionflexure holding structure 506 b (see also FIG. 29A), or another suitableflexible holding structure 506. The flexible holding structure 506 (seeFIG. 30) may comprise a two-piece flexible holding structure 506 c (seeFIG. 30) comprised of two pieces 508 (see FIGS. 29A, 30), including afirst piece 508 a (see FIGS. 29A, 30) attached to a second piece 508 b(see FIGS. 29A, 30), when the flexible holding structure 506 (see FIG.30) is assembled, where the first piece 508 a is a mirror image 509 (seeFIG. 30) of the second piece 508 b. In one version, the two-pieceflexible holding structure 506 c (see FIG. 30) may be comprised ofmirror image plates 510 (see FIG. 30). Each mirror image plate 510 (seeFIG. 30) may comprise a forged plate 510 a (see FIG. 30), an extrudedplate 510 b (see FIG. 30), or another suitable type of plate.

Each of the first side 539 a (see FIG. 29C) and the second side 539 b(see FIG. 29C) of the flexible holding structure 506 preferablycomprises a primary through opening 518 (see FIGS. 29A, 30) configuredto receive, and receiving, the axle element 612. Each of the first side539 a (see FIG. 29C) and the second side 539 b (see FIG. 29C) of theflexible holding structure 506 preferably further comprises a firstsecondary through opening 520 a (see FIG. 29A) configured to receive,and receiving, a fastener 522 (see FIG. 29A), such as in the form of abolt 522 a (see FIG. 29A), or another suitable fastener. Each of thefirst side 539 a (see FIG. 29C) and the second side 539 b (see FIG. 29C)of the flexible holding structure 506 preferably further comprises asecond secondary through opening 520 b (see FIG. 29A) configured toreceive, and receiving, a fastener 522 (see FIG. 29A), such as in theform of a bolt 522 a (see FIG. 29A), or another suitable fastener. Theflexible holding structure 506 (see FIGS. 29A, 30) further has an endthrough opening 538 (see FIGS. 29B, 29C, 30) formed through the firstend 512 a (see FIG. 29B) and the second end 512 b (see FIG. 29B), whenthe flexible holding structure 506 is assembled.

The dual rack and pinion rotational inerter system 500 (see FIGS. 29A,30) preferably further comprises the plurality of rod bearings 540 (seeFIGS. 29A, 30) configured to be inserted into, and inserted along,interior corners 534 (see FIG. 29A) of the flexible holding structure506 (see FIGS. 29A, 30). The rod bearings 540 (see FIGS. 29A, 30) aid inpreventing or minimizing flexing of the two pieces 508 (see FIG. 30) ofthe flexible holding structure 506 (see FIG. 30) when load is applied tothe flexible holding structure 506, and aid in further drawing the racks552 (see FIG. 30) up against the pinion 596 (see FIG. 30) of the dualrack and pinion assembly 550 (see FIG. 30).

As shown in FIG. 30, the dual rack and pinion rotational inerter system500 further comprises the dual rack and pinion assembly 550, discussedin detail above, which is clamped or held, by and between, the flexibleholding structure 506. The dual rack and pinion assembly 550 (see FIG.30) comprises the plurality of racks 552 (see FIG. 30), such as in theform of the first rack 552 a (see FIG. 30) and the second rack 552 b(see FIG. 30). As shown in FIG. 29A, the first rack 552 a is preferablypositioned opposite to the second rack 552 b, with the first pluralityof teeth 570 a on the first rack 552 a facing opposite the secondplurality of teeth 570 b on the second rack 552 b. Each rack 552 (seeFIG. 30) of the dual rack and pinion assembly 550 (see FIG. 30)preferably comprises the spherical bearing attachment portion 558 (seeFIG. 30) and the linear gear portion 560 (see FIG. 30) having theplurality of teeth 570 (see FIG. 30).

The dual rack and pinion assembly 550 (see FIG. 30) further comprisesthe pinion 596 (see FIG. 30), such as in the form of the pinion gear 596a (see FIG. 30), having a plurality of gear teeth 602 (see FIG. 30)formed on the exterior 600 a (see FIG. 29A) of the pinion 596. Thepinion 596 (see FIG. 30), such as the pinion gear 596 a (see FIG. 30),is configured to be engaged to, and is engaged to, and positionedbetween, the first rack 552 a (see FIG. 30) and the second rack 552 b(see FIG. 30). As shown in FIG. 29B, preferably, the gear teeth 602 ofthe pinion 596 engage with the first plurality of teeth 570 a on thefirst rack 552 a facing opposite the second plurality of teeth 570 b onthe second rack 552 b. As shown in FIG. 30, the pinion 596 has athickness 608 and a diameter 610. Preferably, the thickness 608 (seeFIG. 30) of the pinion (see FIG. 30) is equal to, or substantially equalto, the length 658 (see FIG. 29A) of the sleeve element 646 (see FIG.29A). If no sleeve element 646 is present, preferably the thickness 608(see FIG. 30) of the pinion (see FIG. 30) is equal to, or substantiallyequal to, the length 622 (see FIG. 29A) of the central rectangularportion 618 (see FIG. 29A).

The dual rack and pinion rotational inerter system 500 (see FIG. 30)further comprises a first terminal 502 (see FIGS. 27, 29B) and a secondterminal 503 (see FIGS. 27, 29B). The first terminal 502 and the secondterminal 503 preferably comprise spherical bearings 574 (see FIG. 30),such as in the form of spherical ball bearing rods 575 (see FIG. 30).The first terminal 502 (see FIGS. 27, 29B) preferably comprises thefirst spherical bearing 574 a (see FIGS. 27, 29B) having a first end 576a (see FIG. 29A) coupled to the first rack 552 a (see FIGS. 27, 29B, 30)and having a second end 576 b (see FIG. 29A) coupled to the flightcontrol surface 122 (see FIGS. 27, 30), via the pivot element 127 (seeFIGS. 27, 30). The second terminal 503 (see FIGS. 27, 29B) preferablycomprises the second spherical bearing 574 b (see FIGS. 27, 29B) havinga first end 577 a (see FIG. 29A) coupled to the second rack 552 b (seeFIGS. 27, 29B, 30) and having a second end 577 b (see FIG. 29A) coupledto the support structure 116 (see FIGS. 27, 30).

As shown in FIG. 30, the dual rack and pinion rotational inerter system500 further comprises a pair of inertia wheels 660. The pair of inertiawheels 660 (see FIG. 30) preferably comprise the first inertia wheel 660a (see FIGS. 27, 29B) adjacent to the first side 539 a (see FIG. 29B) ofthe flexible holding structure 506 (see FIG. 29B), and preferablycomprises the second inertial wheel 660 b (see FIGS. 27, 29B) adjacentto the second side 539 b (see FIG. 29B) of the flexible holdingstructure 506 (see FIG. 29B). The pair of inertia wheels 660 (see FIGS.29A, 30) each has the through opening 666 (see FIG. 29A) having one of asquare shaped cross-section 668 a (see FIGS. 29A, 30), a circle shapedcross-section 668 b (see FIG. 30), or another suitable shapecross-section. The through opening 666 of each inertia wheel 660 mayhave a smooth interior or may have a spline interior 670 (see FIG. 30).

As shown in FIG. 30, the dual rack and pinion rotational inerter system500 further comprises the axle element 612. The axle element 612 (seeFIGS. 29C, 30) is configured to be inserted through, and is insertedthrough, the first inertial wheel 660 a (see FIG. 29C), the flexibleholding structure 506 (see FIG. 29C), the pinion 596 (see FIG. 29C), andthe second inertial wheel 660 b (see FIG. 29C). The axle element 612(see FIG. 30) couples a rotational movement 611 (see FIG. 30) of thepair of inertia wheels 660 (see FIG. 30) and the pinion 596 (see FIG.30). The axle element 612 (see FIGS. 29A, 30) comprises the centralrectangular portion 618 (see FIGS. 29A, 30), the cylindrical portions632 (see FIG. 29A), the square portions 634 (see FIG. 29A), and thecylindrical threaded end portions 640 (see FIG. 29A). Preferably, thecentral rectangular portion 618 (see FIGS. 29A, 30) has a square shapedcross-section 626 (see FIG. 30). Preferably, the cylindrical portions632 (see FIG. 29A) each have a circle shaped cross-section 631 (see FIG.30). Preferably, the square portions 634 (see FIG. 29A) each have asquare shaped cross-section 638 (see FIG. 30). Preferably, thecylindrical threaded end portions 640 (see FIG. 29A) each have a circleshaped cross-section 644 (see FIG. 30). The axle element 612 (see FIG.30) controls a clamping force 700 (see FIG. 30) of the flexible holdingstructure 506 (see FIG. 30), and controls a slide friction 702 of theinertia wheels 660 (see FIG. 30). To prevent or minimize deflection ofthe flexible holding structure 506, the clamping force 700 (see FIG. 30)may be applied both through the axle element 612 (see FIG. 30) andthrough one or more fasteners 522 (see FIG. 29A), such as bolts 522 a(see FIG. 29A) inserted through the flexible holding structure 506 (seeFIG. 29A).

As shown in FIG. 30, the dual rack and pinion rotational inerter system500 may further comprises a sleeve element 646 configured to surround,and surrounding, the central rectangular portion 618 of the axle element612. Preferably, the sleeve element 646 (see FIGS. 29A, 30) has a length658 (see FIGS. 29A, 30) that is slightly greater than the length 622(see FIGS. 29A, 30) of the central rectangular portion 618, as thesleeve element 646 is designed to cover the central rectangular portion618. Alternatively, the dual rack and pinion rotational inerter system500 does not include the sleeve element 646, and the central rectangularportion 618 is not covered by the sleeve element 646. One or more shims630 (see FIG. 29A) may be applied to one or more side surfaces 628 (seeFIG. 29A) of the central rectangular portion 618 prior to covering thecentral rectangular portion 618 with the sleeve element 646.

Rotation of the flight control surface 122 (see FIG. 30) causestranslational movement 610 (see FIG. 30), via the pivot element 127 (seeFIG. 30), of the first rack 552 a (see FIG. 30) relative to the secondrack 552 b (see FIG. 30), along the longitudinal inerter axis 504 (seeFIG. 27), which causes the rotational movement 611 (see FIG. 30) of thepinion 596 (see FIG. 30) and the pair of inertia wheels 660 (see FIG.30), such that the rotational movement 611 of the pinion 596 is resistedby the pair of inertia wheels 660 and there is no incidental motion 698(see FIG. 30). This results in the dual rack and pinion rotationalinerter system 500 (see FIG. 30) damping movement 694 (see FIG. 30) ofthe flight control surface 122.

The motion of the pinion 596 (see FIG. 30) is resisted by the inertialwheels 660 (see FIG. 30), such that the change of orientation of theracks 552 (see FIG. 30) are only in relation to the longitudinal inerteraxis 504 (see FIG. 27) with the assembly by inducing a resistance force704 (see FIG. 30) to the rotation of the first terminal 502 (see FIG.27) connected to the flight control surface 122 (see FIGS. 27, 30) ofthe aircraft 100 (see FIG. 30). The resistance force 704 (see FIG. 30)is resisted by the inertial wheels 660 (see FIG. 30) with the throughhole 666 (see FIG. 29A) having the square shaped cross-section 668 a(see FIG. 30) and with the axle element 612 (see FIG. 30) having thecentral rectangular portion 618 (see FIG. 30) having the square shapedcross-section 626 (see FIG. 30).

Damping movement 694 (see FIG. 30) of the flight control surface 122(see FIG. 30) preferably provides increased flutter suppression 708 (seeFIG. 30) of the flight control surface 122. This preferably results inan improved hydraulic application stability 710 (see FIG. 30) and anincreased efficient flight control actuation 712 (see FIG. 30). The dualrack and pinion rotational inerter system 500 (see FIG. 30) of theaircraft 100 (see FIG. 30) provides a passive solution 714 (see FIG.30), that is, the dual rack and pinion rotational inerter system 500uses a passive means to change the dynamics of the flight control system120 (see FIG. 30) instead of active control elements, such as one ormore actuators 202 (see FIG. 30) and valve size or diameter of hydraulicactuators 204 (see FIG. 28). The dual rack and pinion rotational inertersystem 500 (see FIG. 30) further provides a reduced backlash 696 (seeFIG. 30) and an increased reliability 706 (see FIG. 30).

Now referring to FIG. 31, FIG. 31 is a flowchart having one or moreoperations that may be included in a method 750 for damping movement 694(see FIG. 30) of a flight control surface 122 (see FIG. 30) of anaircraft 100 (see FIGS. 25, 30). As shown in FIG. 31, the method 750comprises step 752 of installing at least one dual rack and pinionrotational inerter system 500 (see FIGS. 27, 29A) between the flightcontrol surface 122 (see FIG. 27) and the support structure 116 (seeFIG. 27).

As discussed in detail above, the dual rack and pinion rotationalinerter system 500 (see FIGS. 27, 29A, 30) comprises a flexible holdingstructure 506 (see FIGS. 27, 29A) having a plurality of rod bearings 540(see FIG. 29A) inserted into interior corners 534 (see FIG. 29A) of theflexible holding structure 506. The step 752 (see FIG. 31) of installingfurther comprises installing the at least one dual rack and pinionrotational inerter system 500 (see FIGS. 27, 29A, 30), where theflexible holding structure 506 (see FIGS. 27, 29A) comprises a two-pieceflexible holding structure 506 c (see FIG. 30) comprised of mirror imageplates 510 (see FIG. 30), each mirror image plate 510 comprising one of,a forged plate 510 a (see FIG. 30), an extruded plate 510 b (see FIG.30), or another suitable type of plate. The flexible holding structure506 (see FIG. 30) may further comprises a clamping holding structure 506a (see FIG. 30), a thin section flexure holding structure 506 b (seeFIG. 30), or another suitable flexible holding structure 506.

The dual rack and pinion rotational inerter system 500 (see FIGS. 27,29A, 30) further comprises a dual rack and pinion assembly 550 (seeFIGS. 27, 29A) clamped or held by and between the flexible holdingstructure 506 (see FIGS. 27, 29A). The dual rack and pinion assembly 550(see FIGS. 27, 29A) comprises a first rack 552 a (see FIGS. 27, 29A), asecond rack 552 b (see FIGS. 27, 29A) opposite to and facing the firstrack 552 a, and a pinion 596 (see FIGS. 27, 29A) engaged to and betweenthe first rack 552 a and the second rack 552 b. The step 752 (see FIG.31) of installing further comprises installing the at least one dualrack and pinion rotational inerter system 500 (see FIGS. 27, 29A, 30),where the first rack 552 a (see FIG. 29A) has a first plurality of teeth570 a (see FIG. 29A), the second rack 552 b (see FIG. 29A) has a secondplurality of teeth 570 b (see FIG. 29A), and the pinion 596 (see FIG.29A) has a plurality of gear teeth 602 (see FIG. 29A), such that theplurality of gear teeth 602 engage to and between the first plurality ofteeth 570 a and the second plurality of teeth 570 b.

The dual rack and pinion rotational inerter system 500 (see FIGS. 27,29A, 30) further comprises a first terminal 502 (see FIG. 27) coupled tothe first rack 552 a (see FIG. 27) and coupled to the flight controlsurface 122 (see FIG. 27), via a pivot element 127 (see FIG. 27). Thedual rack and pinion rotational inerter system 500 (see FIGS. 27, 29A,30) further comprises a second terminal 503 (see FIG. 27) coupled to thesecond rack 552 b (see FIG. 27), and coupled to the support structure116 (see FIG. 27). The step 752 (see FIG. 31) of installing furthercomprises installing the at least one dual rack and pinion rotationalinerter system 500 (see FIGS. 27, 29A, 30), where the first terminal 502(see FIG. 27) comprises a first spherical bearing 574 a (see FIGS. 27,29A) having a first end 576 a (see FIG. 29A) coupled to the first rack552 a (see FIGS. 27, 29A), and having a second end 576 b (see FIG. 29A)coupled to the flight control surface 122 (see FIG. 27), via the pivotelement 127 (see FIG. 27, and where the second terminal 503 (see FIG.27) comprises a second spherical bearing 574 b (see FIG. 27) having afirst end 577 a (see FIG. 29A) coupled to the second rack 552 b (seeFigured 27, 29A), and having a second end 577 b (see FIG. 29A) coupledto the support structure 116 (see FIG. 27).

The dual rack and pinion rotational inerter system 500 (see FIGS. 27,29A, 30) further comprises a pair of inertia wheels 660 (see FIGS. 27,29A) comprising a first inertia wheel 660 a (see FIGS. 27, 29A) adjacentto a first side 539 a (see FIG. 29A) of the flexible holding structure506 (see FIGS. 27, 29A), and a second inertial wheel 660 b (see FIGS.27, 29A) adjacent to a second side 539 b (see FIG. 29A) of the flexibleholding structure 506.

The dual rack and pinion rotational inerter system 500 (see FIGS. 27,29A, 30) further comprises an axle element 612 (see FIGS. 29A, 29C)inserted through the first inertial wheel 660 a (see FIGS. 29A, 29C),the flexible holding structure 506 (see FIGS. 29A, 29C), the pinion 596(see FIGS. 29A, 29C), and the second inertial wheel 660 b (see FIGS.29A, 29C). The axle element 612 (see FIGS. 29A, 29C) couples arotational movement 611 (see FIG. 30) of the pair of inertia wheels 660(see FIGS. 29A, 29C) and the pinion 596 (see FIGS. 29A, 29C). The step752 (see FIG. 31) of installing further comprises installing the atleast one dual rack and pinion rotational inerter system 500 (see FIGS.27, 29A, 30), further comprising a sleeve element 646 (see FIG. 29A)surrounding a central rectangular portion 618 (see FIG. 29A) of the axleelement 612 (see FIG. 29A).

As shown in FIG. 31, the method 750 further comprises step 754 ofrotating the flight control surface 122 (see FIGS. 27, 30) using one ormore actuators 202 (see FIGS. 27, 30). The flight control surface 122(see FIGS. 27, 30) may comprise an aileron 130 (see FIGS. 27, 30) oranother suitable flight control surface 122.

As shown in FIG. 31, the method 750 further comprises step 756 of usingthe at least one dual rack and pinion rotational inerter 500 (see FIGS.27, 29A, 30) to axially accelerate and pull in a translational movement610 (see FIG. 30) along a longitudinal inerter axis 504 (see FIG. 27),the first rack 552 a (see FIGS. 27, 29A, 30) relative to the second rack552 b (see FIGS. 27, 29A, 30), and to cause the rotational movement 611(see FIG. 30) of the pinion 596 (see FIGS. 27, 29A, 30) and the pair ofinertia wheels 660 (see FIGS. 27, 29A, 30), such that the rotationalmovement 611 of the pinion 596 is resisted by the pair of inertia wheels660 and there is no incidental motion 698 (see FIG. 30). The step 756(see FIG. 31) of using the at least one dual rack and pinion rotationalinerter 500 to axially accelerate and pull the first rack 552 a (seeFIGS. 27, 29A) relative to the second rack 552 b (see FIGS. 27, 29A),further comprises controlling with the axle element 612 (see FIG. 29A) aclamping force 700 (see FIG. 30) of the flexible holding structure 506(see FIGS. 29A, 30).

As shown in FIG. 31, the method 750 further comprises step 758 ofdamping movement 694 (see FIG. 30) of the flight control surface 122(see FIGS. 27, 30), using the at least one dual rack and pinionrotational inerter system 500 (see FIGS. 27, 29A, 30). The step 758 (seeFIG. 31) of damping movement 694 (see FIG. 30) of the flight controlsurface 122 (see FIGS. 27, 30) further comprises damping movement 694 ofthe flight control surface 122 to provide increased flutter suppression708 (see FIG. 30) of the flight control surface 122. This preferablyresults in an improved hydraulic application stability 710 (see FIG. 30)and an increased efficient flight control actuation 712 (see FIG. 30).

Disclosed versions of the dual rack and pinion rotational inerter system500 (see FIGS. 27, 29A-30) and method 750 (see FIG. 31) for dampingmovement 694 (see FIG. 30) of the flight control surface 122 (see FIGS.27, 30) of the aircraft 100 (see FIGS. 25, 30) have numerous advantagessuch as, increased damping of the flight control surface 122, reducedbacklash 696 (see FIG. 30), and increased reliability 706 (see FIG. 30).Increased damping suppresses flutter response of the flight controlsurface 122 (see FIGS. 26, 27, 30) to provide improved hydraulicapplication stability 710 (see FIG. 30) and enable an increasedefficient flight control actuation 712 (see FIG. 30). This solutionpermits the addition of one or more dual rack and pinion rotationalinerter systems 500 (see FIGS. 27, 29A-30) to the flight control system120 (see FIGS. 25, 30), which changes the dynamic characteristic of thehardware under control, rather than complicating the control elementsthemselves.

In addition, disclosed versions of the dual rack and pinion rotationalinerter system 500 (see FIGS. 27, 29A-30) and method 750 (see FIG. 31)may be used to address flutter critical control surface applications onaircraft 100 (see FIG. 25) to further optimize the dual rack and pinionrotational inerter system 500 (see FIGS. 27, 29A-30) design by enablinga two piece flexible holding structure 506 (see FIGS. 27, 29A-30) toclamp a dual rack and pinion assembly 550 (see FIGS. 27, 29A-30). Whenthe dual rack and pinion rotational inerter system 500 is rotated at thefirst terminal 502 (see FIG. 27) connected to the flight control surface122 (see FIG. 27), via the pivot element 127 (see FIG. 27), the racks552 (see FIG. 27) are pulled at either end of the two piece flexibleholding structure 506 along a longitudinal inerter axis 504 (see FIG.27), such as the length of each rack, such that there is no incidentalmotion 698 (see FIG. 30) or incidental rotation. Disclosed versions ofthe dual rack and pinion rotational inerter system 500 (see FIGS. 27,29A-30) and method 750 (see FIG. 31) provide minimum backlash andminimum compliance by achieving damping at a very small deflection. Thedual rack and pinion rotational inerter system 500 (see FIGS. 27,29A-30) has fewer moving parts and has different rendering of size,weight, and power (i.e., reliability), since it is a passive solution714 (see FIG. 30). In addition, disclosed versions of the dual rack andpinion rotational inerter system 500 (see FIGS. 27, 29A-30) and method750 (see FIG. 31) provide render damping in a non-friction manner, asthere is not a thermal issue, just acceleration of the inertia wheel orwheels 660 (see FIGS. 27, 29A-30). The acceleration of the inertia wheelor wheels 660 renders damping movement 694 (see FIG. 30) of the flightcontrol surface 122 (see FIG. 27). Because the inertia wheel or wheels660 (see FIGS. 27, 29A-30), each have a through opening 666 (see FIG.29A) preferably with a square shaped cross-section 668 a (see FIG. 29A)through which an axle element 612 (see FIG. 29A) is inserted, dampingmay be achieved at a very small deflection. This is achieved bycontrolling the dual rack and pinion assembly 550 (see FIGS. 27, 29A-30)with the currently disclosed inertial wheels 660.

The motion of the pinion 596 (see FIG. 29A) is resisted by the inertialwheels 660 (see FIG. 29A), such that the change of orientation of theracks 552 (see FIG. 29A) are only in relation to the longitudinalinerter axis 504 (see FIG. 29A) of the dual rack and pinion rotationalinerter system 500, by inducing resistance force 704 (see FIG. 30) tothe rotation of the first terminal 502 (see FIG. 27) connected to theflight control surface 122 (see FIG. 27) of the aircraft 100 (see FIG.25). The resistance force 704 (see FIG. 30) is resisted by the inertialwheel or wheels 660 (see FIG. 27), each of which comprises the axleelement 612 and the square shaped cross-section 668 a (see FIG. 29A) ofthe through opening 666 (see FIG. 29A). The two pieces 508 (see FIGS.27, 29A) of the flexible holding structure 506 (see FIGS. 27, 29B) canflex by squeezing towards one another, and to prevent deflection, theclamping force 700 (see FIG. 30) may be applied both through the axleelement 612 (see FIG. 29A) and the fasteners 522 (see FIG. 29A) throughthe flexible holding structure 506 (see FIG. 29A). A plurality of rodbearings 540 are preferably installed at each corner of the flexibleholding structure 506 to prevent flexing, thus further drawing the racks552 (see FIG. 29A) up against the pinion 596 (see FIG. 29A).

Moreover, disclosed versions of the dual rack and pinion rotationalinerter system 500 (see FIGS. 17, 29A-30) and method 750 (see FIG. 31)permit the elimination of any stiffness constraint in sizing, whichenables reduced hydraulic system and aircraft size, reduced weight, andreduced power. This solution presents a more space efficient assemblyand method. Further, disclosed versions of the dual rack and pinionrotational inerter system 500 (see FIGS. 27, 29A-30) and method 750 (seeFIG. 31) may improve the performance of aircraft 100 (see FIG. 25) byimproving the actuation system design. Further, the dual rack and pinionrotational inerter system 500 (see FIGS. 27, 29A-30) and method 750 (seeFIG. 31) is a passive solution 714 (see FIG. 30), that is, it uses apassive means to change the dynamics of the flight control system 120(see FIG. 25) instead of the active control elements such as theactuator 202 (see FIG. 28) and valve size or diameter.

In addition, disclosed versions of the dual rack and pinion rotationalinerter system 500 (see FIGS. 27, 29A-30) and method 750 (see FIG. 31)have the advantages of enabling high pressure hydraulic actuator sizingto reduce flow and weight, reducing space required by enabling smalleractuator, valve, and horn element radius, reducing required stiffness toachieve an aero-servo-elasticity goal, addressing force equalization byenabling reduced linear stiffness, increasing compliance that reducesforce-fight for active-active modes, enhancing electro-hydrostaticactuator (EHA) bandwidth without increasing stiffness or heat, andreducing flight control surface resonant amplitude that reduces fatigue.Moreover, disclosed versions of the dual rack and pinion rotationalinerter system 500 (see FIGS. 27, 29A-30) and method 750 (see FIG. 31)have the further advantages of enabling unanticipated kinematic actionto further reduce flow and weight, reducing fatigue by eliminatingamplification of torsion resonance, resolving potentialelectro-hydrostatic actuator (EHA) thermal issues by relaxing stiffnessrequirement, enabling relaxation of an electromechanical actuator (EMA)backlash requirement, including tolerances in automated sizing toevaluate required precision, using variable pressure to achieve weightreduction at comparable reliability, and sizing pressure, e.g., greaterthan 6000 psi (pounds per square inch) which may decrease offtake withsmall weight penalty, where lower offtake enables higher bypass ratio,which improves fuel efficiency. Increased flutter suppression 708 (seeFIG. 30) may provide surface torsion critical damping, and reducedactuator swept volume and smaller actuators, thus providing engine powerofftake and weight and power offtake reduction, where reduced powerofftake enables more fuel efficient engines.

Additional modifications and improvements of the present disclosure maybe apparent to those of ordinary skill in the art. Thus, the particularcombination of parts described and illustrated herein is intended torepresent only certain examples of the present disclosure and is notintended to serve as limitations of alternative examples or deviceswithin the spirit and scope of the disclosure.

What is claimed is:
 1. A dual rack and pinion rotational inerter systemfor damping movement of a flight control surface of an aircraft, thedual rack and pinion rotational inerter system comprising: a flexibleholding structure disposed between the flight control surface and asupport structure of the aircraft; a dual rack and pinion assembly heldby and between the flexible holding structure, the dual rack and pinionassembly comprising a first rack, a second rack, and a pinion engaged toand between the first rack and the second rack; a first terminal coupledto the first rack and coupled to the flight control surface, via a pivotelement, and a second terminal coupled to the second rack, and coupledto the support structure; a pair of inertia wheels comprising a firstinertia wheel adjacent to a first side of the flexible holdingstructure, and a second inertial wheel adjacent to a second side of theflexible holding structure; and an axle element inserted through thefirst inertial wheel, the flexible holding structure, the pinion, andthe second inertial wheel, coupling a rotational movement of the pair ofinertia wheels and the pinion, wherein rotation of the flight controlsurface causes translational movement, via the pivot element, of thefirst rack relative to the second rack, along a longitudinal inerteraxis, which causes the rotational movement of the pinion and the pair ofinertia wheels, such that the rotational movement of the pinion isresisted by the pair of inertia wheels, resulting in the dual rack andpinion rotational inerter system damping movement of the flight controlsurface.
 2. The system of claim 1 further comprising a plurality of rodbearings inserted into interior corners of the flexible holdingstructure.
 3. The system of claim 1 further comprising a sleeve elementsurrounding a central rectangular portion of the axle element.
 4. Thesystem of claim 1 wherein the flexible holding structure comprises oneof a clamping holding structure, and a thin section flexure holdingstructure.
 5. The system of claim 1 wherein the flexible holdingstructure comprises a two-piece flexible holding structure comprised ofa first piece attached to a second piece, wherein the first piece is amirror image of the second piece.
 6. The system of claim 1 wherein thefirst rack has a first plurality of teeth, the second rack has a secondplurality of teeth, and the pinion has a plurality of gear teeth, suchthat the plurality of gear teeth engage to and between the firstplurality of teeth and the second plurality of teeth.
 7. The system ofclaim 1 wherein the first terminal comprises a first spherical bearinghaving a first end coupled to the first rack, and having a second endcoupled to the flight control surface, via the pivot element, andfurther wherein the second terminal comprises a second spherical bearinghaving a first end coupled to the second rack, and having a second endcoupled to the support structure.
 8. The system of claim 1 wherein theaxle element comprises a central rectangular portion, a cylindricalportion attached to each end of the central rectangular portion, asquare portion attached to each end of each cylindrical portion, and acylindrical threaded end portion attached to each end of each squareportion.
 9. The system of claim 1 wherein the pinion has a throughopening having a square shaped cross-section, and each of the pair ofinertia wheels has a through opening having a square shapedcross-section.
 10. An aircraft, comprising: a flight control surfacepivotably coupled to a support structure; one or more actuatorsconfigured to actuate the flight control surface; and at least one dualrack and pinion rotational inerter system for damping movement of theflight control surface of the aircraft, the at least one dual rack andpinion rotational inerter system comprising: a flexible holdingstructure disposed between the flight control surface and the supportstructure of the aircraft; a plurality of rod bearings inserted intointerior corners of the flexible holding structure; a dual rack andpinion assembly clamped by and between the flexible holding structure,the dual rack and pinion assembly comprising a first rack, a secondrack, and a pinion engaged to and between the first rack and the secondrack; a first terminal coupled to the first rack and coupled to theflight control surface, via a pivot element, and a second terminalcoupled to the second rack, and coupled to the support structure; a pairof inertia wheels comprising a first inertia wheel adjacent to a firstside of the flexible holding structure, and a second inertial wheeladjacent to a second side of the flexible holding structure; and an axleelement inserted through the first inertial wheel, the flexible holdingstructure, the pinion, and the second inertial wheel, coupling arotational movement of the pair of inertia wheels and the pinion,wherein rotation of the flight control surface causes translationalmovement, via the pivot element, of the first rack relative to thesecond rack, along a longitudinal inerter axis, which causes therotational movement of the pinion and the pair of inertia wheels, suchthat the rotational movement of the pinion is resisted by the pair ofinertia wheels, resulting in the dual rack and pinion rotational inertersystem damping movement of the flight control surface.
 11. The aircraftof claim 10 wherein the at least one dual rack and pinion rotationalinerter system further comprises a sleeve element surrounding a centralrectangular portion of the axle element.
 12. The aircraft of claim 10wherein the flexible holding structure comprises a two-piece flexibleholding structure comprised of mirror image plates, each mirror imageplate comprising one of, a forged plate, or an extruded plate.
 13. Theaircraft of claim 10 wherein the first terminal comprises a firstspherical bearing having a first end coupled to the first rack, andhaving a second end coupled to the flight control surface, via the pivotelement, and further wherein the second terminal comprises a secondspherical bearing having a first end coupled to the second rack, andhaving a second end coupled to the support structure.
 14. The aircraftof claim 10 wherein the flight control surface comprises an aileron, andthe support structure comprises a wing, a wing portion supportstructure, or a wing spar.
 15. A method for damping movement of a flightcontrol surface of an aircraft, the method comprising the steps of:installing at least one dual rack and pinion rotational inerter systembetween the flight control surface and a support structure of theaircraft; the at least one dual rack and pinion rotational inertersystem comprising: a flexible holding structure having a plurality ofrod bearings inserted into interior corners of the flexible holdingstructure; a dual rack and pinion assembly clamped by and between theflexible holding structure, the dual rack and pinion assembly comprisinga first rack, a second rack, and a pinion engaged to and between thefirst rack and the second rack; a first terminal coupled to the firstrack and coupled to the flight control surface, via a pivot element, anda second terminal coupled to the second rack, and coupled to the supportstructure; a pair of inertia wheels comprising a first inertia wheeladjacent to a first side of the flexible holding structure, and a secondinertial wheel adjacent to a second side of the flexible holdingstructure; and an axle element inserted through the first inertialwheel, the flexible holding structure, the pinion, and the secondinertial wheel, and the axle element coupling a rotational movement ofthe pair of inertia wheels and the pinion, rotating the flight controlsurface using one or more actuators; using the at least one dual rackand pinion rotational inerter to axially accelerate and pull in atranslational movement along a longitudinal inerter axis, the first rackrelative to the second rack, and to cause the rotational movement of thepinion and the pair of inertia wheels, such that the rotational movementof the pinion is resisted by the pair of inertia wheels and there is noincidental motion; and damping movement of the flight control surface,using the at least one dual rack and pinion rotational inerter.
 16. Themethod of claim 15 wherein installing comprises installing the at leastone dual rack and pinion rotational inerter system, further comprising asleeve element surrounding a central rectangular portion of the axleelement.
 17. The method of claim 15 wherein installing comprisesinstalling the at least one dual rack and pinion rotational inertersystem, where the first terminal comprises a first spherical bearinghaving a first end coupled to the first rack, and having a second endcoupled to the flight control surface, via the pivot element, and wherethe second terminal comprises a second spherical bearing having a firstend coupled to the second rack, and having a second end coupled to thesupport structure.
 18. The method of claim 15 wherein installingcomprises installing the at least one dual rack and pinion rotationalinerter system, where the flexible holding structure comprises atwo-piece flexible holding structure comprised of mirror image plates,each mirror image plate comprising one of, a forged plate, or anextruded plate.
 19. The method of claim 15 wherein using the at leastone dual rack and pinion rotational inerter to axially accelerate andpull the first rack relative to the second rack, further comprisescontrolling with the axle element a clamping force of the flexibleholding structure.
 20. The method of claim 15 wherein damping movementof the flight control surface further comprises damping movement of theflight control surface to provide increased flutter suppression of theflight control surface, resulting in an improved hydraulic applicationstability and an increased efficient flight control actuation.